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 Topics FrontPage FriCAS FriCASIntegration RichExp2 <-- You are here. Examples involving exponential function from Albert Rich testsuite. fricas)set messages time on  fricas)set break resume  fricas)set output tex off  fricas)set output algebra on -- Integrands of the form x^m F^(c (a+b x)^n) -- n>0 integrate(f^(c*(a+b*x)^2)*x^m, x) x 2 2 2 ++ m (%A b + 2 %A a b + a )c (1) | %A f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.04 (IN) + 0.04 (EV) + 0.18 (OT) = 0.26 sec integrate(f^(c*(a+b*x)^2)*x^3, x) (2) +------------+ | 2 3 2 2 +---+ (b x + a)\|- b c log(f) (- 2 a b c log(f) + 3 a b c log(f))\|%pi erf(------------------------) b + 2 2 2 ((2 b c x - 2 a b c x + 2 a c)log(f) - 2) * 2 2 2 +------------+ (b c x + 2 a b c x + a c)log(f) | 2 %e \|- b c log(f) / +------------+ 4 2 2 | 2 4 b c log(f) \|- b c log(f) Type: Union(Expression(Integer),...) fricasTime: 0.01 (IN) + 0.02 (OT) = 0.03 sec integrate(f^(c*(a+b*x)^2)*x^2, x) (3) +------------+ | 2 2 +---+ (b x + a)\|- b c log(f) (2 a b c log(f) - b)\|%pi erf(------------------------) b + 2 2 2 +------------+ (b c x + 2 a b c x + a c)log(f) | 2 (2 b x - 2 a)%e \|- b c log(f) / +------------+ 3 | 2 4 b c log(f)\|- b c log(f) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c*(a+b*x)^2)*x, x) (4) +------------+ | 2 +---+ (b x + a)\|- b c log(f) - a b c log(f)\|%pi erf(------------------------) b + 2 2 2 +------------+ (b c x + 2 a b c x + a c)log(f) | 2 %e \|- b c log(f) / +------------+ 2 | 2 2 b c log(f)\|- b c log(f) Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec integrate(f^(c*(a+b*x)^2), x) +------------+ | 2 +---+ (b x + a)\|- b c log(f) \|%pi erf(------------------------) b (5) ----------------------------------- +------------+ | 2 2 \|- b c log(f) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c*(a+b*x)^2)/x, x) 2 2 2 x (%A b + 2 %A a b + a )c ++ f (6) | ------------------------- d%A ++ %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c*(a+b*x)^2)/x^2, x) 2 2 2 x (%A b + 2 %A a b + a )c ++ f (7) | ------------------------- d%A ++ 2 %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (IN) = 0.01 sec integrate(f^(c*(a+b*x)^2)/x^3, x) 2 2 2 x (%A b + 2 %A a b + a )c ++ f (8) | ------------------------- d%A ++ 3 %A Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c*(a+b*x)^3)*x^m, x) x 3 3 2 2 2 3 ++ m (%A b + 3 %A a b + 3 %A a b + a )c (9) | %A f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c*(a+b*x)^3)*x^2, x) (10) 3 3 2 2 2 3 +------------+2 (b c x + 3 a b c x + 3 a b c x + a c)log(f) 3| 3 %e \|- b c log(f) + - 2 1 3 3 2 2 2 3 a b c log(f)Gamma(-,(- b c x - 3 a b c x - 3 a b c x - a c)log(f)) 3 * +------------+ 3| 3 \|- b c log(f) + 2 2 3 3 2 2 2 3 2 a b c log(f)Gamma(-,(- b c x - 3 a b c x - 3 a b c x - a c)log(f)) 3 / +------------+2 3 3| 3 3 b c log(f)\|- b c log(f) Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec integrate(f^(c*(a+b*x)^3)*x, x) (11) +------------+ 1 3 3 2 2 2 3 3| 3 a Gamma(-,(- b c x - 3 a b c x - 3 a b c x - a c)log(f))\|- b c log(f) 3 + 2 3 3 2 2 2 3 - b Gamma(-,(- b c x - 3 a b c x - 3 a b c x - a c)log(f)) 3 / +------------+2 3| 3 3 b \|- b c log(f) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c*(a+b*x)^3), x) 1 3 3 2 2 2 3 Gamma(-,(- b c x - 3 a b c x - 3 a b c x - a c)log(f)) 3 (12) - -------------------------------------------------------- +------------+ 3| 3 3 \|- b c log(f) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c*(a+b*x)^3)/x, x) 3 3 2 2 2 3 x (%A b + 3 %A a b + 3 %A a b + a )c ++ f (13) | ------------------------------------- d%A ++ %A Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c*(a+b*x)^3)/x^2, x) 3 3 2 2 2 3 x (%A b + 3 %A a b + 3 %A a b + a )c ++ f (14) | ------------------------------------- d%A ++ 2 %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c*(a+b*x)^3)/x^3, x) 3 3 2 2 2 3 x (%A b + 3 %A a b + 3 %A a b + a )c ++ f (15) | ------------------------------------- d%A ++ 3 %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^m, x) x 3 3 2 2 2 3 ++ %A b + 3 %A a b + 3 %A a b + a m (16) | %e %A d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^4, x) (17) 3 3 2 2 2 3 +----+2 2 2 2 b x + 3 a b x + 3 a b x + a 3| 3 (3 b x - 6 a b x + 9 a )%e \|- b + +----+ 4 1 3 3 2 2 2 3 3| 3 (- 3 a - 4 a)b Gamma(-,- b x - 3 a b x - 3 a b x - a )\|- b 3 + 3 2 2 3 3 2 2 2 3 (12 a + 2)b Gamma(-,- b x - 3 a b x - 3 a b x - a ) 3 / +----+2 5 3| 3 9 b \|- b Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^3, x) (18) 3 3 2 2 2 3 +----+2 b x + 3 a b x + 3 a b x + a 3| 3 (3 b x - 6 a)%e \|- b + +----+ 3 1 3 3 2 2 2 3 3| 3 (3 a + 1)b Gamma(-,- b x - 3 a b x - 3 a b x - a )\|- b 3 + 2 2 2 3 3 2 2 2 3 - 9 a b Gamma(-,- b x - 3 a b x - 3 a b x - a ) 3 / +----+2 4 3| 3 9 b \|- b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x^2, x) (19) 3 3 2 2 2 3 +----+2 b x + 3 a b x + 3 a b x + a 3| 3 %e \|- b + +----+ 2 1 3 3 2 2 2 3 3| 3 - a b Gamma(-,- b x - 3 a b x - 3 a b x - a )\|- b 3 + 2 2 3 3 2 2 2 3 2 a b Gamma(-,- b x - 3 a b x - 3 a b x - a ) 3 / +----+2 3 3| 3 3 b \|- b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)*x, x) (20) +----+ 1 3 3 2 2 2 3 3| 3 a Gamma(-,- b x - 3 a b x - 3 a b x - a )\|- b 3 + 2 3 3 2 2 2 3 - b Gamma(-,- b x - 3 a b x - 3 a b x - a ) 3 / +----+2 3| 3 3 b \|- b Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3), x) 1 3 3 2 2 2 3 Gamma(-,- b x - 3 a b x - 3 a b x - a ) 3 (21) - ----------------------------------------- +----+ 3| 3 3 \|- b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(a^3+3*a^2*b*x+3*a*b^2*x^2+b^3*x^3)/x, x) 3 3 2 2 2 3 x %A b + 3 %A a b + 3 %A a b + a ++ %e (22) | ----------------------------------- d%A ++ %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^sqrt(5+3*x), x) +-------+ +-------+ \|3 x + 5 (2 \|3 x + 5 - 2)%e (23) ------------------------------ 3 Type: Union(Expression(Integer),...) fricasTime: 0 sec -- n<0 integrate(f^(c/(a+b*x))*x^m, x) c x -------- ++ m %A b + a (24) | %A f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(f^(c/(a+b*x))*x^4, x) (25) 4 4 4 2 3 2 3 2 3 3 (b c x + a c )log(f) + (b c x - 18 a b c x - 19 a c )log(f) + 3 2 3 2 2 2 2 2 3 2 2 (2 b c x - 14 a b c x + 86 a b c x + 102 a c )log(f) + 4 4 3 3 2 2 2 3 4 (6 b c x - 16 a b c x + 36 a b c x - 96 a b c x - 154 a c)log(f) + 5 5 5 24 b x + 24 a * c log(f) -------- b x + a %e + 5 5 4 4 2 3 3 3 2 2 - c log(f) + 20 a c log(f) - 120 a c log(f) + 240 a c log(f) + 4 - 120 a c log(f) * c log(f) Ei(--------) b x + a / 5 120 b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x))*x^3, x) (26) 3 3 3 2 2 2 2 2 2 2 (b c x + a c )log(f) + (b c x - 10 a b c x - 11 a c )log(f) + 3 3 2 2 2 3 4 4 4 (2 b c x - 6 a b c x + 18 a b c x + 26 a c)log(f) + 6 b x - 6 a * c log(f) -------- b x + a %e + 4 4 3 3 2 2 2 3 c log(f) (- c log(f) + 12 a c log(f) - 36 a c log(f) + 24 a c log(f))Ei(--------) b x + a / 4 24 b Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(f^(c/(a+b*x))*x^2, x) (27) 2 2 2 2 2 2 3 3 (b c x + a c )log(f) + (b c x - 4 a b c x - 5 a c)log(f) + 2 b x + 3 2 a * c log(f) -------- b x + a %e + 3 3 2 2 2 c log(f) (- c log(f) + 6 a c log(f) - 6 a c log(f))Ei(--------) b x + a / 3 6 b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x))*x, x) (28) c log(f) -------- 2 2 2 b x + a ((b c x + a c)log(f) + b x - a )%e + 2 2 c log(f) (- c log(f) + 2 a c log(f))Ei(--------) b x + a / 2 2 b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x)), x) c log(f) -------- b x + a c log(f) (b x + a)%e - c log(f)Ei(--------) b x + a (29) ------------------------------------------ b Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(f^(c/(a+b*x))/x, x) c log(f) -------- b c x log(f) a c log(f) (30) Ei(- ------------)%e - Ei(--------) 2 b x + a a b x + a Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x))/x^2, x) c log(f) c log(f) -------- -------- b c x log(f) a 2 b x + a - b c x log(f)Ei(- ------------)%e + (- a b x - a )%e 2 a b x + a (31) --------------------------------------------------------------------- 2 a x Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x))/x^3, x) (32) c log(f) -------- 2 2 2 2 2 2 b c x log(f) a (b c x log(f) + 2 a b c x log(f))Ei(- ------------)%e 2 a b x + a + c log(f) -------- 2 2 2 2 2 2 4 b x + a ((a b c x + a b c x)log(f) + a b x - a )%e / 4 2 2 a x Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c/(a+b*x)^2)*x^m, x) c --------------------- x 2 2 2 ++ m %A b + 2 %A a b + a (33) | %A f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x)^2)*x^4, x) (34) +----------+ | c log(f) b |- -------- | 2 3 3 2 2 2 4 +---+ \| b (- 4 c log(f) - 60 a c log(f) - 15 a c log(f))\|%pi erf(--------------) b x + a + 2 2 2 2 (4 b c x + 4 a b c )log(f) + 4 3 3 2 2 2 3 6 5 (2 b c x - 9 a b c x + 36 a b c x + 47 a b c)log(f) + 3 b x + 5 3 a b * c log(f) ------------------- 2 2 2 b x + 2 a b x + a %e + 2 2 3 c log(f) (15 a b c log(f) + 30 a b c log(f))Ei(-------------------) 2 2 2 b x + 2 a b x + a * +----------+ | c log(f) |- -------- | 2 \| b / +----------+ 6 | c log(f) 15 b |- -------- | 2 \| b Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(f^(c/(a+b*x)^2)*x^3, x) (35) +----------+ | c log(f) b |- -------- | 2 2 2 3 +---+ \| b (8 a c log(f) + 4 a c log(f))\|%pi erf(--------------) b x + a + 3 2 2 2 5 4 4 ((b c x - 6 a b c x - 7 a b c)log(f) + b x - a b) * c log(f) ------------------- 2 2 2 b x + 2 a b x + a %e + 2 2 2 c log(f) (- b c log(f) - 6 a b c log(f))Ei(-------------------) 2 2 2 b x + 2 a b x + a * +----------+ | c log(f) |- -------- | 2 \| b / +----------+ 5 | c log(f) 4 b |- -------- | 2 \| b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x)^2)*x^2, x) (36) +----------+ | c log(f) b |- -------- | 2 2 2 2 +---+ \| b (- 2 c log(f) - 3 a c log(f))\|%pi erf(--------------) b x + a + c log(f) ------------------- 2 2 2 2 4 3 3 b x + 2 a b x + a ((2 b c x + 2 a b c)log(f) + b x + a b)%e + c log(f) 3 a b c log(f)Ei(-------------------) 2 2 2 b x + 2 a b x + a * +----------+ | c log(f) |- -------- | 2 \| b / +----------+ 4 | c log(f) 3 b |- -------- | 2 \| b Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c/(a+b*x)^2)*x, x) (37) +----------+ | c log(f) b |- -------- | 2 +---+ \| b 2 a c log(f)\|%pi erf(--------------) b x + a + c log(f) ------------------- 2 2 2 3 2 2 b x + 2 a b x + a c log(f) ((b x - a b)%e - b c log(f)Ei(-------------------)) 2 2 2 b x + 2 a b x + a * +----------+ | c log(f) |- -------- | 2 \| b / +----------+ 3 | c log(f) 2 b |- -------- | 2 \| b Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c/(a+b*x)^2), x) (38) +----------+ | c log(f) b |- -------- | 2 +---+ \| b - c log(f)\|%pi erf(--------------) b x + a + c log(f) ------------------- 2 2 2 +----------+ 2 b x + 2 a b x + a | c log(f) (b x + a b)%e |- -------- | 2 \| b / +----------+ 2 | c log(f) b |- -------- | 2 \| b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x)^2)/x, x) c --------------------- 2 2 2 x %A b + 2 %A a b + a ++ f (39) | ---------------------- d%A ++ %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec integrate(f^(c/(a+b*x)^2)/x^2, x) c --------------------- 2 2 2 x %A b + 2 %A a b + a ++ f (40) | ---------------------- d%A ++ 2 %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c/(a+b*x)^2)/x^3, x) c --------------------- 2 2 2 x %A b + 2 %A a b + a ++ f (41) | ---------------------- d%A ++ 3 %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c/(a+b*x)^3)*x^m, x) c --------------------------------- x 3 3 2 2 2 3 ++ m %A b + 3 %A a b + 3 %A a b + a (42) | %A f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(f^(c/(a+b*x)^3)*x^4, x) (43) 4 2 3 2 2 7 5 5 2 ((3 b c x - 24 a b c x - 27 a b c)log(f) + 2 b x + 2 a b ) * c log(f) ------------------------------ 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a %e + 2 2 c log(f) - 20 a b c log(f)Ei(------------------------------) 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a * +----------+2 | c log(f) |- -------- 3| 3 \| b + 2 2 3 (3 b c log(f) - 20 a b c log(f)) * +----------+ 1 c log(f) | c log(f) Gamma(-,- ------------------------------) |- -------- 3 3 3 2 2 2 3 3| 3 b x + 3 a b x + 3 a b x + a \| b + 2 2 4 2 c log(f) (- 30 a c log(f) + 10 a c log(f))Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a / +----------+2 7 | c log(f) 10 b |- -------- 3| 3 \| b Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(f^(c/(a+b*x)^3)*x^3, x) (44) 3 2 6 4 4 2 ((3 b c x + 3 a b c)log(f) + b x - a b ) * c log(f) ------------------------------ 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a %e + 2 c log(f) 4 a b c log(f)Ei(------------------------------) 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a * +----------+2 | c log(f) |- -------- 3| 3 \| b + +----------+ 2 1 c log(f) | c log(f) 6 a b c log(f)Gamma(-,- ------------------------------) |- -------- 3 3 3 2 2 2 3 3| 3 b x + 3 a b x + 3 a b x + a \| b + 2 2 3 2 c log(f) (3 c log(f) - 4 a c log(f))Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a / +----------+2 6 | c log(f) 4 b |- -------- 3| 3 \| b Type: Union(Expression(Integer),...) fricasTime: 0.04 (EV) + 0.02 (OT) = 0.06 sec integrate(f^(c/(a+b*x)^3)*x^2, x) (45) c log(f) ------------------------------ 3 3 2 2 2 3 5 3 3 2 b x + 3 a b x + 3 a b x + a (b x + a b )%e + 2 c log(f) - b c log(f)Ei(------------------------------) 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a * +----------+2 | c log(f) |- -------- 3| 3 \| b + +----------+ 1 c log(f) | c log(f) - 3 a b c log(f)Gamma(-,- ------------------------------) |- -------- 3 3 3 2 2 2 3 3| 3 b x + 3 a b x + 3 a b x + a \| b + 2 2 c log(f) 3 a c log(f)Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a / +----------+2 5 | c log(f) 3 b |- -------- 3| 3 \| b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x)^3)*x, x) (46) c log(f) ------------------------------ 3 3 2 2 2 3 +----------+2 4 2 2 2 b x + 3 a b x + 3 a b x + a | c log(f) (b x - a b )%e |- -------- 3| 3 \| b + +----------+ 1 c log(f) | c log(f) b c log(f)Gamma(-,- ------------------------------) |- -------- 3 3 3 2 2 2 3 3| 3 b x + 3 a b x + 3 a b x + a \| b + 2 c log(f) - 2 a c log(f)Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a / +----------+2 4 | c log(f) 2 b |- -------- 3| 3 \| b Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(f^(c/(a+b*x)^3), x) (47) c log(f) ------------------------------ 3 3 2 2 2 3 +----------+2 3 2 b x + 3 a b x + 3 a b x + a | c log(f) (b x + a b )%e |- -------- 3| 3 \| b + 2 c log(f) c log(f)Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 b x + 3 a b x + 3 a b x + a / +----------+2 3 | c log(f) b |- -------- 3| 3 \| b Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x)^3)/x, x) c --------------------------------- 3 3 2 2 2 3 x %A b + 3 %A a b + 3 %A a b + a ++ f (48) | ---------------------------------- d%A ++ %A Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c/(a+b*x)^3)/x^2, x) c --------------------------------- 3 3 2 2 2 3 x %A b + 3 %A a b + 3 %A a b + a ++ f (49) | ---------------------------------- d%A ++ 2 %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (IN) + 0.01 (OT) = 0.02 sec integrate(f^(c/(a+b*x)^3)/x^3, x) c --------------------------------- 3 3 2 2 2 3 x %A b + 3 %A a b + 3 %A a b + a ++ f (50) | ---------------------------------- d%A ++ 3 %A Type: Union(Expression(Integer),...) fricasTime: 0 sec -- n symbolic integrate(f^(c*(a+b*x)^n)*x^m, x) x n ++ m c (%A b + a) (51) | %A f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (IN) + 0.02 (OT) = 0.03 sec integrate(f^(c*(a+b*x)^n)*x^3, x) x n ++ 3 c (%A b + a) (52) | %A f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c*(a+b*x)^n)*x^2, x) x n ++ 2 c (%A b + a) (53) | %A f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c*(a+b*x)^n)*x, x) x n ++ c (%A b + a) (54) | %A f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (IN) = 0.01 sec integrate(f^(c*(a+b*x)^n), x) x n ++ c (%A b + a) (55) | f d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c*(a+b*x)^n)/x, x) n x c (%A b + a) ++ f (56) | -------------- d%A ++ %A Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(c*(a+b*x)^n)/x^2, x) n x c (%A b + a) ++ f (57) | -------------- d%A ++ 2 %A Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(f^(c*(a+b*x)^n)/x^3, x) n x c (%A b + a) ++ f (58) | -------------- d%A ++ 3 %A Type: Union(Expression(Integer),...) fricasTime: 0 sec -- Integrands of the form (c+d x)^m F^(a+b (c+d x)^n) -- n>0 integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^m, x) (59) m + 1 2 2 2 Gamma(-----,(- b d x - 2 b c d x - b c )log(F)) 2 * (- m + 1)log(- b log(F)) + 2 a log(F) ------------------------------------- 2 %e / 2 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^11, x) (60) 5 10 10 5 9 9 5 2 8 8 5 3 7 7 5 4 6 6 b d x + 10 b c d x + 45 b c d x + 120 b c d x + 210 b c d x + 5 5 5 5 5 6 4 4 5 7 3 3 5 8 2 2 252 b c d x + 210 b c d x + 120 b c d x + 45 b c d x + 5 9 5 10 10 b c d x + b c * 5 log(F) + 4 8 8 4 7 7 4 2 6 6 4 3 5 5 - 5 b d x - 40 b c d x - 140 b c d x - 280 b c d x + 4 4 4 4 4 5 3 3 4 6 2 2 4 7 4 8 - 350 b c d x - 280 b c d x - 140 b c d x - 40 b c d x - 5 b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 20 b d x + 120 b c d x + 300 b c d x + 400 b c d x + 3 4 2 2 3 5 3 6 300 b c d x + 120 b c d x + 20 b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 (- 60 b d x - 240 b c d x - 360 b c d x - 240 b c d x - 60 b c ) * 2 log(F) + 2 2 2 (120 b d x + 240 b c d x + 120 b c )log(F) - 120 * 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e / 6 6 2 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^9, x) (61) 4 8 8 4 7 7 4 2 6 6 4 3 5 5 4 4 4 4 b d x + 8 b c d x + 28 b c d x + 56 b c d x + 70 b c d x + 4 5 3 3 4 6 2 2 4 7 4 8 56 b c d x + 28 b c d x + 8 b c d x + b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 - 4 b d x - 24 b c d x - 60 b c d x - 80 b c d x - 60 b c d x + 3 5 3 6 - 24 b c d x - 4 b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (12 b d x + 48 b c d x + 72 b c d x + 48 b c d x + 12 b c )log(F) + 2 2 2 (- 24 b d x - 48 b c d x - 24 b c )log(F) + 24 * 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e / 5 5 2 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^7, x) (62) 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 b d x + 6 b c d x + 15 b c d x + 20 b c d x + 15 b c d x + 3 5 3 6 6 b c d x + b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 3 b d x - 12 b c d x - 18 b c d x - 12 b c d x - 3 b c )log(F) + 2 2 2 (6 b d x + 12 b c d x + 6 b c )log(F) - 6 * 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e / 4 4 2 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^5, x) (63) 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (b d x + 4 b c d x + 6 b c d x + 4 b c d x + b c )log(F) + 2 2 2 (- 2 b d x - 4 b c d x - 2 b c )log(F) + 2 * 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e / 3 3 2 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^3, x) (64) 2 2 2 ((b d x + 2 b c d x + b c )log(F) - 1) * 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e / 2 2 2 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x), x) 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e (65) --------------------------------------- 2 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x), x) 2 2 2 a log(F) Ei((b d x + 2 b c d x + b c )log(F))%e (66) ----------------------------------------------- 2 d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^3, x) (67) 2 2 2 (b d x + 2 b c d x + b c + a)log(F) - %e + 2 2 2 2 2 2 (b d x + 2 b c d x + b c )log(F)Ei((b d x + 2 b c d x + b c )log(F)) * a log(F) %e / 3 2 2 2 2 d x + 4 c d x + 2 c d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^5, x) (68) 2 2 2 ((- b d x - 2 b c d x - b c )log(F) - 1) * 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (b d x + 4 b c d x + 6 b c d x + 4 b c d x + b c )log(F) * 2 2 2 a log(F) Ei((b d x + 2 b c d x + b c )log(F))%e / 5 4 4 3 2 3 2 3 2 4 4 d x + 16 c d x + 24 c d x + 16 c d x + 4 c d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^7, x) (69) 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- b d x - 4 b c d x - 6 b c d x - 4 b c d x - b c )log(F) + 2 2 2 (- b d x - 2 b c d x - b c )log(F) - 2 * 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 b d x + 6 b c d x + 15 b c d x + 20 b c d x + 15 b c d x + 3 5 3 6 6 b c d x + b c * 3 2 2 2 a log(F) log(F) Ei((b d x + 2 b c d x + b c )log(F))%e / 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 12 d x + 72 c d x + 180 c d x + 240 c d x + 180 c d x + 72 c d x + 6 12 c d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^9, x) (70) 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 - b d x - 6 b c d x - 15 b c d x - 20 b c d x - 15 b c d x + 3 5 3 6 - 6 b c d x - b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- b d x - 4 b c d x - 6 b c d x - 4 b c d x - b c )log(F) + 2 2 2 (- 2 b d x - 4 b c d x - 2 b c )log(F) - 6 * 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e + 4 8 8 4 7 7 4 2 6 6 4 3 5 5 4 4 4 4 b d x + 8 b c d x + 28 b c d x + 56 b c d x + 70 b c d x + 4 5 3 3 4 6 2 2 4 7 4 8 56 b c d x + 28 b c d x + 8 b c d x + b c * 4 2 2 2 a log(F) log(F) Ei((b d x + 2 b c d x + b c )log(F))%e / 9 8 8 7 2 7 6 3 6 5 4 5 4 48 d x + 384 c d x + 1344 c d x + 2688 c d x + 3360 c d x + 5 4 3 6 3 2 7 2 8 2688 c d x + 1344 c d x + 384 c d x + 48 c d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^11, x) (71) 4 8 8 4 7 7 4 2 6 6 4 3 5 5 4 4 4 4 - b d x - 8 b c d x - 28 b c d x - 56 b c d x - 70 b c d x + 4 5 3 3 4 6 2 2 4 7 4 8 - 56 b c d x - 28 b c d x - 8 b c d x - b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 - b d x - 6 b c d x - 15 b c d x - 20 b c d x - 15 b c d x + 3 5 3 6 - 6 b c d x - b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 2 b d x - 8 b c d x - 12 b c d x - 8 b c d x - 2 b c )log(F) + 2 2 2 (- 6 b d x - 12 b c d x - 6 b c )log(F) - 24 * 2 2 2 (b d x + 2 b c d x + b c + a)log(F) %e + 5 10 10 5 9 9 5 2 8 8 5 3 7 7 5 4 6 6 b d x + 10 b c d x + 45 b c d x + 120 b c d x + 210 b c d x + 5 5 5 5 5 6 4 4 5 7 3 3 5 8 2 2 5 9 252 b c d x + 210 b c d x + 120 b c d x + 45 b c d x + 10 b c d x + 5 10 b c * 5 2 2 2 a log(F) log(F) Ei((b d x + 2 b c d x + b c )log(F))%e / 11 10 10 9 2 9 8 3 8 7 4 7 6 240 d x + 2400 c d x + 10800 c d x + 28800 c d x + 50400 c d x + 5 6 5 6 5 4 7 4 3 8 3 2 9 2 60480 c d x + 50400 c d x + 28800 c d x + 10800 c d x + 2400 c d x + 10 240 c d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^12, x) (72) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) 10395 d\|%pi %e erf(------------------------) d + 5 11 11 5 10 10 5 2 9 9 5 3 8 8 64 b d x + 704 b c d x + 3520 b c d x + 10560 b c d x + 5 4 7 7 5 5 6 6 5 6 5 5 5 7 4 4 21120 b c d x + 29568 b c d x + 29568 b c d x + 21120 b c d x + 5 8 3 3 5 9 2 2 5 10 5 11 10560 b c d x + 3520 b c d x + 704 b c d x + 64 b c * 5 log(F) + 4 9 9 4 8 8 4 2 7 7 4 3 6 6 - 352 b d x - 3168 b c d x - 12672 b c d x - 29568 b c d x + 4 4 5 5 4 5 4 4 4 6 3 3 - 44352 b c d x - 44352 b c d x - 29568 b c d x + 4 7 2 2 4 8 4 9 - 12672 b c d x - 3168 b c d x - 352 b c * 4 log(F) + 3 7 7 3 6 6 3 2 5 5 3 3 4 4 1584 b d x + 11088 b c d x + 33264 b c d x + 55440 b c d x + 3 4 3 3 3 5 2 2 3 6 3 7 55440 b c d x + 33264 b c d x + 11088 b c d x + 1584 b c * 3 log(F) + 2 5 5 2 4 4 2 2 3 3 2 3 2 2 - 5544 b d x - 27720 b c d x - 55440 b c d x - 55440 b c d x + 2 4 2 5 - 27720 b c d x - 5544 b c * 2 log(F) + 3 3 2 2 2 3 (13860 b d x + 41580 b c d x + 41580 b c d x + 13860 b c )log(F) + - 20790 d x - 20790 c * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 6 6 | 2 128 b d log(F) \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^10, x) (73) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) - 945 d\|%pi %e erf(------------------------) d + 4 9 9 4 8 8 4 2 7 7 4 3 6 6 32 b d x + 288 b c d x + 1152 b c d x + 2688 b c d x + 4 4 5 5 4 5 4 4 4 6 3 3 4 7 2 2 4032 b c d x + 4032 b c d x + 2688 b c d x + 1152 b c d x + 4 8 4 9 288 b c d x + 32 b c * 4 log(F) + 3 7 7 3 6 6 3 2 5 5 3 3 4 4 - 144 b d x - 1008 b c d x - 3024 b c d x - 5040 b c d x + 3 4 3 3 3 5 2 2 3 6 3 7 - 5040 b c d x - 3024 b c d x - 1008 b c d x - 144 b c * 3 log(F) + 2 5 5 2 4 4 2 2 3 3 2 3 2 2 504 b d x + 2520 b c d x + 5040 b c d x + 5040 b c d x + 2 4 2 5 2520 b c d x + 504 b c * 2 log(F) + 3 3 2 2 2 3 (- 1260 b d x - 3780 b c d x - 3780 b c d x - 1260 b c )log(F) + 1890 d x + 1890 c * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 5 5 | 2 64 b d log(F) \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^8, x) (74) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) 105 d\|%pi %e erf(------------------------) d + 3 7 7 3 6 6 3 2 5 5 3 3 4 4 16 b d x + 112 b c d x + 336 b c d x + 560 b c d x + 3 4 3 3 3 5 2 2 3 6 3 7 560 b c d x + 336 b c d x + 112 b c d x + 16 b c * 3 log(F) + 2 5 5 2 4 4 2 2 3 3 2 3 2 2 - 56 b d x - 280 b c d x - 560 b c d x - 560 b c d x + 2 4 2 5 - 280 b c d x - 56 b c * 2 log(F) + 3 3 2 2 2 3 (140 b d x + 420 b c d x + 420 b c d x + 140 b c )log(F) - 210 d x + - 210 c * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 4 4 | 2 32 b d log(F) \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^6, x) (75) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) - 15 d\|%pi %e erf(------------------------) d + 2 5 5 2 4 4 2 2 3 3 2 3 2 2 2 4 8 b d x + 40 b c d x + 80 b c d x + 80 b c d x + 40 b c d x + 2 5 8 b c * 2 log(F) + 3 3 2 2 2 3 (- 20 b d x - 60 b c d x - 60 b c d x - 20 b c )log(F) + 30 d x + 30 c * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 3 3 | 2 16 b d log(F) \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^4, x) (76) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) 3 d\|%pi %e erf(------------------------) d + 3 3 2 2 2 3 ((4 b d x + 12 b c d x + 12 b c d x + 4 b c )log(F) - 6 d x - 6 c) * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 2 2 | 2 8 b d log(F) \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)*(c+d*x)^2, x) (77) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) - d\|%pi %e erf(------------------------) d + 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 (2 d x + 2 c)%e \|- b d log(F) / +------------+ | 2 4 b d log(F)\|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2), x) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d (78) --------------------------------------------- +------------+ | 2 2 \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^2, x) (79) +------------+ | 2 2 +---+ a log(F) (d x + c)\|- b d log(F) (b d x + b c d)log(F)\|%pi %e erf(------------------------) d + 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 - %e \|- b d log(F) / +------------+ 2 | 2 (d x + c d)\|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^4, x) (80) 2 4 3 2 3 2 2 2 2 2 3 2 +---+ a log(F) (2 b d x + 6 b c d x + 6 b c d x + 2 b c d)log(F) \|%pi %e * +------------+ | 2 (d x + c)\|- b d log(F) erf(------------------------) d + 2 2 2 ((- 2 b d x - 4 b c d x - 2 b c )log(F) - 1) * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 4 3 3 2 2 2 3 | 2 (3 d x + 9 c d x + 9 c d x + 3 c d)\|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^6, x) (81) 3 6 5 3 5 4 3 2 4 3 3 3 3 2 3 4 2 4 b d x + 20 b c d x + 40 b c d x + 40 b c d x + 20 b c d x + 3 5 4 b c d * +------------+ | 2 3 +---+ a log(F) (d x + c)\|- b d log(F) log(F) \|%pi %e erf(------------------------) d + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 4 b d x - 16 b c d x - 24 b c d x - 16 b c d x - 4 b c )log(F) + 2 2 2 (- 2 b d x - 4 b c d x - 2 b c )log(F) - 3 * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / 6 5 5 4 2 4 3 3 3 2 4 2 5 (15 d x + 75 c d x + 150 c d x + 150 c d x + 75 c d x + 15 c d) * +------------+ | 2 \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^8, x) (82) 4 8 7 4 7 6 4 2 6 5 4 3 5 4 4 4 4 3 8 b d x + 56 b c d x + 168 b c d x + 280 b c d x + 280 b c d x + 4 5 3 2 4 6 2 4 7 168 b c d x + 56 b c d x + 8 b c d * +------------+ | 2 4 +---+ a log(F) (d x + c)\|- b d log(F) log(F) \|%pi %e erf(------------------------) d + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 - 8 b d x - 48 b c d x - 120 b c d x - 160 b c d x + 3 4 2 2 3 5 3 6 - 120 b c d x - 48 b c d x - 8 b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 4 b d x - 16 b c d x - 24 b c d x - 16 b c d x - 4 b c )log(F) + 2 2 2 (- 6 b d x - 12 b c d x - 6 b c )log(F) - 15 * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / 8 7 7 6 2 6 5 3 5 4 4 4 3 105 d x + 735 c d x + 2205 c d x + 3675 c d x + 3675 c d x + 5 3 2 6 2 7 2205 c d x + 735 c d x + 105 c d * +------------+ | 2 \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^10, x) (83) 5 10 9 5 9 8 5 2 8 7 5 3 7 6 16 b d x + 144 b c d x + 576 b c d x + 1344 b c d x + 5 4 6 5 5 5 5 4 5 6 4 3 5 7 3 2 2016 b c d x + 2016 b c d x + 1344 b c d x + 576 b c d x + 5 8 2 5 9 144 b c d x + 16 b c d * +------------+ | 2 5 +---+ a log(F) (d x + c)\|- b d log(F) log(F) \|%pi %e erf(------------------------) d + 4 8 8 4 7 7 4 2 6 6 4 3 5 5 - 16 b d x - 128 b c d x - 448 b c d x - 896 b c d x + 4 4 4 4 4 5 3 3 4 6 2 2 4 7 - 1120 b c d x - 896 b c d x - 448 b c d x - 128 b c d x + 4 8 - 16 b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 - 8 b d x - 48 b c d x - 120 b c d x - 160 b c d x + 3 4 2 2 3 5 3 6 - 120 b c d x - 48 b c d x - 8 b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 (- 12 b d x - 48 b c d x - 72 b c d x - 48 b c d x - 12 b c ) * 2 log(F) + 2 2 2 (- 30 b d x - 60 b c d x - 30 b c )log(F) - 105 * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / 10 9 9 8 2 8 7 3 7 6 4 6 5 945 d x + 8505 c d x + 34020 c d x + 79380 c d x + 119070 c d x + 5 5 4 6 4 3 7 3 2 8 2 9 119070 c d x + 79380 c d x + 34020 c d x + 8505 c d x + 945 c d * +------------+ | 2 \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b*(c+d*x)^2)/(c+d*x)^12, x) (84) 6 12 11 6 11 10 6 2 10 9 6 3 9 8 32 b d x + 352 b c d x + 1760 b c d x + 5280 b c d x + 6 4 8 7 6 5 7 6 6 6 6 5 6 7 5 4 10560 b c d x + 14784 b c d x + 14784 b c d x + 10560 b c d x + 6 8 4 3 6 9 3 2 6 10 2 6 11 5280 b c d x + 1760 b c d x + 352 b c d x + 32 b c d * +------------+ | 2 6 +---+ a log(F) (d x + c)\|- b d log(F) log(F) \|%pi %e erf(------------------------) d + 5 10 10 5 9 9 5 2 8 8 5 3 7 7 - 32 b d x - 320 b c d x - 1440 b c d x - 3840 b c d x + 5 4 6 6 5 5 5 5 5 6 4 4 5 7 3 3 - 6720 b c d x - 8064 b c d x - 6720 b c d x - 3840 b c d x + 5 8 2 2 5 9 5 10 - 1440 b c d x - 320 b c d x - 32 b c * 5 log(F) + 4 8 8 4 7 7 4 2 6 6 4 3 5 5 - 16 b d x - 128 b c d x - 448 b c d x - 896 b c d x + 4 4 4 4 4 5 3 3 4 6 2 2 4 7 - 1120 b c d x - 896 b c d x - 448 b c d x - 128 b c d x + 4 8 - 16 b c * 4 log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 - 24 b d x - 144 b c d x - 360 b c d x - 480 b c d x + 3 4 2 2 3 5 3 6 - 360 b c d x - 144 b c d x - 24 b c * 3 log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 (- 60 b d x - 240 b c d x - 360 b c d x - 240 b c d x - 60 b c ) * 2 log(F) + 2 2 2 (- 210 b d x - 420 b c d x - 210 b c )log(F) - 945 * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / 12 11 11 10 2 10 9 3 9 8 10395 d x + 114345 c d x + 571725 c d x + 1715175 c d x + 4 8 7 5 7 6 6 6 5 7 5 4 3430350 c d x + 4802490 c d x + 4802490 c d x + 3430350 c d x + 8 4 3 9 3 2 10 2 11 1715175 c d x + 571725 c d x + 114345 c d x + 10395 c d * +------------+ | 2 \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^m, x) (85) m + 1 3 3 2 2 2 3 Gamma(-----,(- b d x - 3 b c d x - 3 b c d x - b c )log(F)) 3 * (- m + 2)log(- b log(F)) + 3 a log(F) ------------------------------------- 3 %e / 3 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^17, x) (86) 5 15 15 5 14 14 5 2 13 13 5 3 12 12 b d x + 15 b c d x + 105 b c d x + 455 b c d x + 5 4 11 11 5 5 10 10 5 6 9 9 5 7 8 8 1365 b c d x + 3003 b c d x + 5005 b c d x + 6435 b c d x + 5 8 7 7 5 9 6 6 5 10 5 5 5 11 4 4 6435 b c d x + 5005 b c d x + 3003 b c d x + 1365 b c d x + 5 12 3 3 5 13 2 2 5 14 5 15 455 b c d x + 105 b c d x + 15 b c d x + b c * 5 log(F) + 4 12 12 4 11 11 4 2 10 10 4 3 9 9 - 5 b d x - 60 b c d x - 330 b c d x - 1100 b c d x + 4 4 8 8 4 5 7 7 4 6 6 6 4 7 5 5 - 2475 b c d x - 3960 b c d x - 4620 b c d x - 3960 b c d x + 4 8 4 4 4 9 3 3 4 10 2 2 4 11 - 2475 b c d x - 1100 b c d x - 330 b c d x - 60 b c d x + 4 12 - 5 b c * 4 log(F) + 3 9 9 3 8 8 3 2 7 7 3 3 6 6 20 b d x + 180 b c d x + 720 b c d x + 1680 b c d x + 3 4 5 5 3 5 4 4 3 6 3 3 3 7 2 2 2520 b c d x + 2520 b c d x + 1680 b c d x + 720 b c d x + 3 8 3 9 180 b c d x + 20 b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 - 60 b d x - 360 b c d x - 900 b c d x - 1200 b c d x + 2 4 2 2 2 5 2 6 - 900 b c d x - 360 b c d x - 60 b c * 2 log(F) + 3 3 2 2 2 3 (120 b d x + 360 b c d x + 360 b c d x + 120 b c )log(F) - 120 * 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e / 6 6 3 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^14, x) (87) 4 12 12 4 11 11 4 2 10 10 4 3 9 9 b d x + 12 b c d x + 66 b c d x + 220 b c d x + 4 4 8 8 4 5 7 7 4 6 6 6 4 7 5 5 495 b c d x + 792 b c d x + 924 b c d x + 792 b c d x + 4 8 4 4 4 9 3 3 4 10 2 2 4 11 4 12 495 b c d x + 220 b c d x + 66 b c d x + 12 b c d x + b c * 4 log(F) + 3 9 9 3 8 8 3 2 7 7 3 3 6 6 - 4 b d x - 36 b c d x - 144 b c d x - 336 b c d x + 3 4 5 5 3 5 4 4 3 6 3 3 3 7 2 2 - 504 b c d x - 504 b c d x - 336 b c d x - 144 b c d x + 3 8 3 9 - 36 b c d x - 4 b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 12 b d x + 72 b c d x + 180 b c d x + 240 b c d x + 2 4 2 2 2 5 2 6 180 b c d x + 72 b c d x + 12 b c * 2 log(F) + 3 3 2 2 2 3 (- 24 b d x - 72 b c d x - 72 b c d x - 24 b c )log(F) + 24 * 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e / 5 5 3 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^11, x) (88) 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 b d x + 9 b c d x + 36 b c d x + 84 b c d x + 126 b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 126 b c d x + 84 b c d x + 36 b c d x + 9 b c d x + b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 - 3 b d x - 18 b c d x - 45 b c d x - 60 b c d x - 45 b c d x + 2 5 2 6 - 18 b c d x - 3 b c * 2 log(F) + 3 3 2 2 2 3 (6 b d x + 18 b c d x + 18 b c d x + 6 b c )log(F) - 6 * 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e / 4 4 3 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^8, x) (89) 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 b d x + 6 b c d x + 15 b c d x + 20 b c d x + 15 b c d x + 2 5 2 6 6 b c d x + b c * 2 log(F) + 3 3 2 2 2 3 (- 2 b d x - 6 b c d x - 6 b c d x - 2 b c )log(F) + 2 * 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e / 3 3 3 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (IN) = 0.01 sec integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^5, x) (90) 3 3 2 2 2 3 ((b d x + 3 b c d x + 3 b c d x + b c )log(F) - 1) * 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e / 2 2 3 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^2, x) 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e (91) ---------------------------------------------------- 3 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^3)/(c+d*x), x) 3 3 2 2 2 3 a log(F) Ei((b d x + 3 b c d x + 3 b c d x + b c )log(F))%e (92) ------------------------------------------------------------ 3 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^4, x) (93) 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) - %e + 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c )log(F) * 3 3 2 2 2 3 a log(F) Ei((b d x + 3 b c d x + 3 b c d x + b c )log(F))%e / 4 3 3 2 2 2 3 3 d x + 9 c d x + 9 c d x + 3 c d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^7, x) (94) 3 3 2 2 2 3 ((- b d x - 3 b c d x - 3 b c d x - b c )log(F) - 1) * 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 b d x + 6 b c d x + 15 b c d x + 20 b c d x + 15 b c d x + 2 5 2 6 6 b c d x + b c * 2 3 3 2 2 2 3 a log(F) log(F) Ei((b d x + 3 b c d x + 3 b c d x + b c )log(F))%e / 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 6 d x + 36 c d x + 90 c d x + 120 c d x + 90 c d x + 36 c d x + 6 c d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^10, x) (95) 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 - b d x - 6 b c d x - 15 b c d x - 20 b c d x - 15 b c d x + 2 5 2 6 - 6 b c d x - b c * 2 log(F) + 3 3 2 2 2 3 (- b d x - 3 b c d x - 3 b c d x - b c )log(F) - 2 * 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e + 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 b d x + 9 b c d x + 36 b c d x + 84 b c d x + 126 b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 126 b c d x + 84 b c d x + 36 b c d x + 9 b c d x + b c * 3 3 3 2 2 2 3 a log(F) log(F) Ei((b d x + 3 b c d x + 3 b c d x + b c )log(F))%e / 10 9 9 8 2 8 7 3 7 6 4 6 5 18 d x + 162 c d x + 648 c d x + 1512 c d x + 2268 c d x + 5 5 4 6 4 3 7 3 2 8 2 9 2268 c d x + 1512 c d x + 648 c d x + 162 c d x + 18 c d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) + 0.01 (OT) = 0.03 sec integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^13, x) (96) 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 - b d x - 9 b c d x - 36 b c d x - 84 b c d x - 126 b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 - 126 b c d x - 84 b c d x - 36 b c d x - 9 b c d x - b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 - b d x - 6 b c d x - 15 b c d x - 20 b c d x - 15 b c d x + 2 5 2 6 - 6 b c d x - b c * 2 log(F) + 3 3 2 2 2 3 (- 2 b d x - 6 b c d x - 6 b c d x - 2 b c )log(F) - 6 * 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e + 4 12 12 4 11 11 4 2 10 10 4 3 9 9 b d x + 12 b c d x + 66 b c d x + 220 b c d x + 4 4 8 8 4 5 7 7 4 6 6 6 4 7 5 5 495 b c d x + 792 b c d x + 924 b c d x + 792 b c d x + 4 8 4 4 4 9 3 3 4 10 2 2 4 11 4 12 495 b c d x + 220 b c d x + 66 b c d x + 12 b c d x + b c * 4 3 3 2 2 2 3 a log(F) log(F) Ei((b d x + 3 b c d x + 3 b c d x + b c )log(F))%e / 13 12 12 11 2 11 10 3 10 9 4 9 8 72 d x + 864 c d x + 4752 c d x + 15840 c d x + 35640 c d x + 5 8 7 6 7 6 7 6 5 8 5 4 9 4 3 57024 c d x + 66528 c d x + 57024 c d x + 35640 c d x + 15840 c d x + 10 3 2 11 2 12 4752 c d x + 864 c d x + 72 c d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^16, x) (97) 4 12 12 4 11 11 4 2 10 10 4 3 9 9 - b d x - 12 b c d x - 66 b c d x - 220 b c d x + 4 4 8 8 4 5 7 7 4 6 6 6 4 7 5 5 - 495 b c d x - 792 b c d x - 924 b c d x - 792 b c d x + 4 8 4 4 4 9 3 3 4 10 2 2 4 11 4 12 - 495 b c d x - 220 b c d x - 66 b c d x - 12 b c d x - b c * 4 log(F) + 3 9 9 3 8 8 3 2 7 7 3 3 6 6 3 4 5 5 - b d x - 9 b c d x - 36 b c d x - 84 b c d x - 126 b c d x + 3 5 4 4 3 6 3 3 3 7 2 2 3 8 3 9 - 126 b c d x - 84 b c d x - 36 b c d x - 9 b c d x - b c * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 - 2 b d x - 12 b c d x - 30 b c d x - 40 b c d x + 2 4 2 2 2 5 2 6 - 30 b c d x - 12 b c d x - 2 b c * 2 log(F) + 3 3 2 2 2 3 (- 6 b d x - 18 b c d x - 18 b c d x - 6 b c )log(F) - 24 * 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) %e + 5 15 15 5 14 14 5 2 13 13 5 3 12 12 b d x + 15 b c d x + 105 b c d x + 455 b c d x + 5 4 11 11 5 5 10 10 5 6 9 9 5 7 8 8 1365 b c d x + 3003 b c d x + 5005 b c d x + 6435 b c d x + 5 8 7 7 5 9 6 6 5 10 5 5 5 11 4 4 6435 b c d x + 5005 b c d x + 3003 b c d x + 1365 b c d x + 5 12 3 3 5 13 2 2 5 14 5 15 455 b c d x + 105 b c d x + 15 b c d x + b c * 5 3 3 2 2 2 3 a log(F) log(F) Ei((b d x + 3 b c d x + 3 b c d x + b c )log(F))%e / 16 15 15 14 2 14 13 3 13 12 360 d x + 5400 c d x + 37800 c d x + 163800 c d x + 4 12 11 5 11 10 6 10 9 7 9 8 491400 c d x + 1081080 c d x + 1801800 c d x + 2316600 c d x + 8 8 7 9 7 6 10 6 5 11 5 4 2316600 c d x + 1801800 c d x + 1081080 c d x + 491400 c d x + 12 4 3 13 3 2 14 2 15 163800 c d x + 37800 c d x + 5400 c d x + 360 c d Type: Union(Expression(Integer),...) fricasTime: 0.03 (EV) = 0.03 sec integrate(F^(a+b*(c+d*x)^3)*(c+d*x)^3, x) (98) 3 3 2 2 2 3 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) (3 d x + 3 c)%e * +------------+ 3| 3 \|- b d log(F) + a log(F) 1 3 3 2 2 2 3 d %e Gamma(-,(- b d x - 3 b c d x - 3 b c d x - b c )log(F)) 3 / +------------+ 3| 3 9 b d log(F)\|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^3)*(c+d*x), x) (99) a log(F) 2 3 3 2 2 2 3 d %e Gamma(-,(- b d x - 3 b c d x - 3 b c d x - b c )log(F)) 3 - --------------------------------------------------------------------- +------------+2 3| 3 3 \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^3), x) (100) a log(F) 1 3 3 2 2 2 3 %e Gamma(-,(- b d x - 3 b c d x - 3 b c d x - b c )log(F)) 3 - ------------------------------------------------------------------- +------------+ 3| 3 3 \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^2, x) (101) 3 3 2 2 2 3 +------------+2 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) 3| 3 - %e \|- b d log(F) + 3 2 a log(F) (- b d x - b c d )log(F)%e * 2 3 3 2 2 2 3 Gamma(-,(- b d x - 3 b c d x - 3 b c d x - b c )log(F)) 3 / +------------+2 2 3| 3 (d x + c d)\|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^3, x) (102) 3 3 2 2 2 3 +------------+ (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) 3| 3 - %e \|- b d log(F) + 3 2 2 2 a log(F) (- b d x - 2 b c d x - b c d)log(F)%e * 1 3 3 2 2 2 3 Gamma(-,(- b d x - 3 b c d x - 3 b c d x - b c )log(F)) 3 / +------------+ 3 2 2 2 3| 3 (2 d x + 4 c d x + 2 c d)\|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^3)/(c+d*x)^5, x) (103) 3 3 2 2 2 3 ((- 3 b d x - 9 b c d x - 9 b c d x - 3 b c )log(F) - 1) * 3 3 2 2 2 3 +------------+2 (b d x + 3 b c d x + 3 b c d x + b c + a)log(F) 3| 3 %e \|- b d log(F) + 2 6 4 2 5 3 2 2 4 2 2 3 3 2 4 2 2 (- 3 b d x - 12 b c d x - 18 b c d x - 12 b c d x - 3 b c d )log(F) * a log(F) 2 3 3 2 2 2 3 %e Gamma(-,(- b d x - 3 b c d x - 3 b c d x - b c )log(F)) 3 / +------------+2 5 4 4 3 2 3 2 3 2 4 3| 3 (4 d x + 16 c d x + 24 c d x + 16 c d x + 4 c d)\|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(f^(a+b*(c+d*x)^(1/2)), x) +-------+ +-------+ b log(f)\|d x + c + a log(f) (2 b log(f)\|d x + c - 2)%e (104) --------------------------------------------------------- 2 2 b d log(f) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(f^(a+b*(c+d*x)^(1/3)), x) (105) 2 2 3+-------+2 3+-------+ (3 b log(f) \|d x + c - 6 b log(f)\|d x + c + 6) * 3+-------+ b log(f)\|d x + c + a log(f) %e / 3 3 b d log(f) Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec -- n<0 integrate(F^(a+b/(c+d*x))*(c+d*x)^m, x) %A a d + a c + b x ---------------- ++ %A d + c m (106) | F (%A d + c) d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x))*(c+d*x)^4, x) (107) 4 4 4 3 2 2 3 3 2 3 (b d x + b c)log(F) + (b d x + 2 b c d x + b c )log(F) + 2 3 3 2 2 2 2 2 2 3 2 (2 b d x + 6 b c d x + 6 b c d x + 2 b c )log(F) + 4 4 3 3 2 2 2 3 4 (6 b d x + 24 b c d x + 36 b c d x + 24 b c d x + 6 b c )log(F) + 5 5 4 4 2 3 3 3 2 2 4 5 24 d x + 120 c d x + 240 c d x + 240 c d x + 120 c d x + 24 c * (a d x + a c + b)log(F) ----------------------- d x + c %e + 5 5 b log(F) a log(F) - b log(F) Ei(--------)%e d x + c / 120 d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x))*(c+d*x)^3, x) (108) 3 3 3 2 2 2 2 2 2 2 (b d x + b c)log(F) + (b d x + 2 b c d x + b c )log(F) + 3 3 2 2 2 3 4 4 (2 b d x + 6 b c d x + 6 b c d x + 2 b c )log(F) + 6 d x + 3 3 2 2 2 3 4 24 c d x + 36 c d x + 24 c d x + 6 c * (a d x + a c + b)log(F) ----------------------- d x + c %e + 4 4 b log(F) a log(F) - b log(F) Ei(--------)%e d x + c / 24 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b/(c+d*x))*(c+d*x)^2, x) (109) 2 2 2 2 2 2 3 3 (b d x + b c)log(F) + (b d x + 2 b c d x + b c )log(F) + 2 d x + 2 2 2 3 6 c d x + 6 c d x + 2 c * (a d x + a c + b)log(F) ----------------------- d x + c %e + 3 3 b log(F) a log(F) - b log(F) Ei(--------)%e d x + c / 6 d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x))*(c+d*x), x) (110) (a d x + a c + b)log(F) ----------------------- 2 2 2 d x + c ((b d x + b c)log(F) + d x + 2 c d x + c )%e + 2 2 b log(F) a log(F) - b log(F) Ei(--------)%e d x + c / 2 d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x)), x) (a d x + a c + b)log(F) ----------------------- d x + c b log(F) a log(F) (d x + c)%e - b log(F)Ei(--------)%e d x + c (111) ------------------------------------------------------------------- d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b/(c+d*x))/(c+d*x), x) b log(F) a log(F) Ei(--------)%e d x + c (112) - ---------------------- d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x))/(c+d*x)^2, x) (a d x + a c + b)log(F) ----------------------- d x + c %e (113) - ------------------------- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x))/(c+d*x)^3, x) (a d x + a c + b)log(F) ----------------------- d x + c (- b log(F) + d x + c)%e (114) ----------------------------------------------- 2 2 2 2 (b d x + b c d)log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x))/(c+d*x)^4, x) (115) 2 2 2 2 2 (- b log(F) + (2 b d x + 2 b c)log(F) - 2 d x - 4 c d x - 2 c ) * (a d x + a c + b)log(F) ----------------------- d x + c %e / 3 3 2 3 2 3 2 3 (b d x + 2 b c d x + b c d)log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b/(c+d*x))/(c+d*x)^5, x) (116) 3 3 2 2 2 - b log(F) + (3 b d x + 3 b c)log(F) + 2 2 2 3 3 2 2 (- 6 b d x - 12 b c d x - 6 b c )log(F) + 6 d x + 18 c d x + 2 3 18 c d x + 6 c * (a d x + a c + b)log(F) ----------------------- d x + c %e / 4 4 3 4 3 2 4 2 2 4 3 4 (b d x + 3 b c d x + 3 b c d x + b c d)log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x))/(c+d*x)^6, x) (117) 4 4 3 3 3 - b log(F) + (4 b d x + 4 b c)log(F) + 2 2 2 2 2 2 2 (- 12 b d x - 24 b c d x - 12 b c )log(F) + 3 3 2 2 2 3 4 4 (24 b d x + 72 b c d x + 72 b c d x + 24 b c )log(F) - 24 d x + 3 3 2 2 2 3 4 - 96 c d x - 144 c d x - 96 c d x - 24 c * (a d x + a c + b)log(F) ----------------------- d x + c %e / 5 5 4 5 4 3 5 2 3 2 5 3 2 5 4 5 (b d x + 4 b c d x + 6 b c d x + 4 b c d x + b c d)log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b/(c+d*x))/(c+d*x)^7, x) (118) 5 5 4 4 4 - b log(F) + (5 b d x + 5 b c)log(F) + 3 2 2 3 3 2 3 (- 20 b d x - 40 b c d x - 20 b c )log(F) + 2 3 3 2 2 2 2 2 2 3 2 (60 b d x + 180 b c d x + 180 b c d x + 60 b c )log(F) + 4 4 3 3 2 2 2 3 4 (- 120 b d x - 480 b c d x - 720 b c d x - 480 b c d x - 120 b c ) * log(F) + 5 5 4 4 2 3 3 3 2 2 4 5 120 d x + 600 c d x + 1200 c d x + 1200 c d x + 600 c d x + 120 c * (a d x + a c + b)log(F) ----------------------- d x + c %e / 6 6 5 6 5 4 6 2 4 3 6 3 3 2 6 4 2 6 5 (b d x + 5 b c d x + 10 b c d x + 10 b c d x + 5 b c d x + b c d) * 6 log(F) Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^m, x) 2 2 2 %A a d + 2 %A a c d + a c + b ------------------------------- x 2 2 2 ++ %A d + 2 %A c d + c m (119) | F (%A d + c) d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^9, x) (120) 4 2 2 4 4 2 4 (b d x + 2 b c d x + b c )log(F) + 3 4 4 3 3 3 3 2 2 2 3 3 3 4 3 (b d x + 4 b c d x + 6 b c d x + 4 b c d x + b c )log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 2 b d x + 12 b c d x + 30 b c d x + 40 b c d x + 30 b c d x + 2 5 2 6 12 b c d x + 2 b c * 2 log(F) + 8 8 7 7 2 6 6 3 5 5 6 b d x + 48 b c d x + 168 b c d x + 336 b c d x + 4 4 4 5 3 3 6 2 2 7 8 420 b c d x + 336 b c d x + 168 b c d x + 48 b c d x + 6 b c * log(F) + 10 10 9 9 2 8 8 3 7 7 4 6 6 24 d x + 240 c d x + 1080 c d x + 2880 c d x + 5040 c d x + 5 5 5 6 4 4 7 3 3 8 2 2 9 6048 c d x + 5040 c d x + 2880 c d x + 1080 c d x + 240 c d x + 10 24 c * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 d x + 2 c d x + c %e + 5 5 b log(F) a log(F) - b log(F) Ei(-------------------)%e 2 2 2 d x + 2 c d x + c / 240 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^7, x) (121) 3 2 2 3 3 2 3 (b d x + 2 b c d x + b c )log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (b d x + 4 b c d x + 6 b c d x + 4 b c d x + b c )log(F) + 6 6 5 5 2 4 4 3 3 3 4 2 2 2 b d x + 12 b c d x + 30 b c d x + 40 b c d x + 30 b c d x + 5 6 12 b c d x + 2 b c * log(F) + 8 8 7 7 2 6 6 3 5 5 4 4 4 6 d x + 48 c d x + 168 c d x + 336 c d x + 420 c d x + 5 3 3 6 2 2 7 8 336 c d x + 168 c d x + 48 c d x + 6 c * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 d x + 2 c d x + c %e + 4 4 b log(F) a log(F) - b log(F) Ei(-------------------)%e 2 2 2 d x + 2 c d x + c / 48 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^5, x) (122) 2 2 2 2 2 2 2 (b d x + 2 b c d x + b c )log(F) + 4 4 3 3 2 2 2 3 4 6 6 (b d x + 4 b c d x + 6 b c d x + 4 b c d x + b c )log(F) + 2 d x + 5 5 2 4 4 3 3 3 4 2 2 5 6 12 c d x + 30 c d x + 40 c d x + 30 c d x + 12 c d x + 2 c * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 d x + 2 c d x + c %e + 3 3 b log(F) a log(F) - b log(F) Ei(-------------------)%e 2 2 2 d x + 2 c d x + c / 12 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^3, x) (123) 2 2 2 4 4 3 3 2 2 2 (b d x + 2 b c d x + b c )log(F) + d x + 4 c d x + 6 c d x + 3 4 4 c d x + c * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 d x + 2 c d x + c %e + 2 2 b log(F) a log(F) - b log(F) Ei(-------------------)%e 2 2 2 d x + 2 c d x + c / 4 d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x), x) (124) 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 2 2 2 d x + 2 c d x + c (d x + 2 c d x + c )%e + b log(F) a log(F) - b log(F)Ei(-------------------)%e 2 2 2 d x + 2 c d x + c / 2 d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x), x) b log(F) a log(F) Ei(-------------------)%e 2 2 2 d x + 2 c d x + c (125) - --------------------------------- 2 d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^3, x) 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 d x + 2 c d x + c %e (126) - --------------------------------------- 2 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^5, x) (127) 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 2 2 2 d x + 2 c d x + c (- b log(F) + d x + 2 c d x + c )%e ------------------------------------------------------------------------- 2 3 2 2 2 2 2 2 (2 b d x + 4 b c d x + 2 b c d)log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^7, x) (128) 2 2 2 2 2 4 4 3 3 - b log(F) + (2 b d x + 4 b c d x + 2 b c )log(F) - 2 d x - 8 c d x + 2 2 2 3 4 - 12 c d x - 8 c d x - 2 c * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 d x + 2 c d x + c %e / 3 5 4 3 4 3 3 2 3 2 3 3 2 3 4 3 (2 b d x + 8 b c d x + 12 b c d x + 8 b c d x + 2 b c d)log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^9, x) (129) 3 3 2 2 2 2 2 2 2 - b log(F) + (3 b d x + 6 b c d x + 3 b c )log(F) + 4 4 3 3 2 2 2 3 4 (- 6 b d x - 24 b c d x - 36 b c d x - 24 b c d x - 6 b c )log(F) + 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 6 d x + 36 c d x + 90 c d x + 120 c d x + 90 c d x + 36 c d x + 6 c * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 d x + 2 c d x + c %e / 4 7 6 4 6 5 4 2 5 4 4 3 4 3 4 4 3 2 2 b d x + 12 b c d x + 30 b c d x + 40 b c d x + 30 b c d x + 4 5 2 4 6 12 b c d x + 2 b c d * 4 log(F) Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^11, x) (130) 4 4 3 2 2 3 3 2 3 - b log(F) + (4 b d x + 8 b c d x + 4 b c )log(F) + 2 4 4 2 3 3 2 2 2 2 2 3 2 4 2 (- 12 b d x - 48 b c d x - 72 b c d x - 48 b c d x - 12 b c )log(F) + 6 6 5 5 2 4 4 3 3 3 24 b d x + 144 b c d x + 360 b c d x + 480 b c d x + 4 2 2 5 6 360 b c d x + 144 b c d x + 24 b c * log(F) + 8 8 7 7 2 6 6 3 5 5 4 4 4 - 24 d x - 192 c d x - 672 c d x - 1344 c d x - 1680 c d x + 5 3 3 6 2 2 7 8 - 1344 c d x - 672 c d x - 192 c d x - 24 c * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 d x + 2 c d x + c %e / 5 9 8 5 8 7 5 2 7 6 5 3 6 5 5 4 5 4 2 b d x + 16 b c d x + 56 b c d x + 112 b c d x + 140 b c d x + 5 5 4 3 5 6 3 2 5 7 2 5 8 112 b c d x + 56 b c d x + 16 b c d x + 2 b c d * 5 log(F) Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) + 0.01 (OT) = 0.03 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^13, x) (131) 5 5 4 2 2 4 4 2 4 - b log(F) + (5 b d x + 10 b c d x + 5 b c )log(F) + 3 4 4 3 3 3 3 2 2 2 3 3 3 4 (- 20 b d x - 80 b c d x - 120 b c d x - 80 b c d x - 20 b c ) * 3 log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 60 b d x + 360 b c d x + 900 b c d x + 1200 b c d x + 2 4 2 2 2 5 2 6 900 b c d x + 360 b c d x + 60 b c * 2 log(F) + 8 8 7 7 2 6 6 3 5 5 - 120 b d x - 960 b c d x - 3360 b c d x - 6720 b c d x + 4 4 4 5 3 3 6 2 2 7 - 8400 b c d x - 6720 b c d x - 3360 b c d x - 960 b c d x + 8 - 120 b c * log(F) + 10 10 9 9 2 8 8 3 7 7 4 6 6 120 d x + 1200 c d x + 5400 c d x + 14400 c d x + 25200 c d x + 5 5 5 6 4 4 7 3 3 8 2 2 9 30240 c d x + 25200 c d x + 14400 c d x + 5400 c d x + 1200 c d x + 10 120 c * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 d x + 2 c d x + c %e / 6 11 10 6 10 9 6 2 9 8 6 3 8 7 6 4 7 6 2 b d x + 20 b c d x + 90 b c d x + 240 b c d x + 420 b c d x + 6 5 6 5 6 6 5 4 6 7 4 3 6 8 3 2 6 9 2 504 b c d x + 420 b c d x + 240 b c d x + 90 b c d x + 20 b c d x + 6 10 2 b c d * 6 log(F) Type: Union(Expression(Integer),...) fricasTime: 0.11 (EV) = 0.11 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^10, x) (132) +----------+ | b log(F) d |- -------- | 2 6 6 +---+ a log(F) \| d - 32 b log(F) \|%pi %e erf(--------------) d x + c + 5 2 5 5 (32 b d x + 32 b c d)log(F) + 4 4 3 4 3 2 4 2 2 4 3 4 (16 b d x + 48 b c d x + 48 b c d x + 16 b c d)log(F) + 3 6 5 3 5 4 3 2 4 3 3 3 3 2 24 b d x + 120 b c d x + 240 b c d x + 240 b c d x + 3 4 2 3 5 120 b c d x + 24 b c d * 3 log(F) + 2 8 7 2 7 6 2 2 6 5 2 3 5 4 60 b d x + 420 b c d x + 1260 b c d x + 2100 b c d x + 2 4 4 3 2 5 3 2 2 6 2 2 7 2100 b c d x + 1260 b c d x + 420 b c d x + 60 b c d * 2 log(F) + 10 9 9 8 2 8 7 3 7 6 210 b d x + 1890 b c d x + 7560 b c d x + 17640 b c d x + 4 6 5 5 5 4 6 4 3 7 3 2 26460 b c d x + 26460 b c d x + 17640 b c d x + 7560 b c d x + 8 2 9 1890 b c d x + 210 b c d * log(F) + 12 11 11 10 2 10 9 3 9 8 945 d x + 10395 c d x + 51975 c d x + 155925 c d x + 4 8 7 5 7 6 6 6 5 7 5 4 311850 c d x + 436590 c d x + 436590 c d x + 311850 c d x + 8 4 3 9 3 2 10 2 11 155925 c d x + 51975 c d x + 10395 c d x + 945 c d * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 10395 d |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.03 (EV) + 0.01 (OT) = 0.04 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^8, x) (133) +----------+ | b log(F) d |- -------- | 2 5 5 +---+ a log(F) \| d - 16 b log(F) \|%pi %e erf(--------------) d x + c + 4 2 4 4 (16 b d x + 16 b c d)log(F) + 3 4 3 3 3 2 3 2 2 3 3 3 (8 b d x + 24 b c d x + 24 b c d x + 8 b c d)log(F) + 2 6 5 2 5 4 2 2 4 3 2 3 3 2 12 b d x + 60 b c d x + 120 b c d x + 120 b c d x + 2 4 2 2 5 60 b c d x + 12 b c d * 2 log(F) + 8 7 7 6 2 6 5 3 5 4 30 b d x + 210 b c d x + 630 b c d x + 1050 b c d x + 4 4 3 5 3 2 6 2 7 1050 b c d x + 630 b c d x + 210 b c d x + 30 b c d * log(F) + 10 9 9 8 2 8 7 3 7 6 4 6 5 105 d x + 945 c d x + 3780 c d x + 8820 c d x + 13230 c d x + 5 5 4 6 4 3 7 3 2 8 2 9 13230 c d x + 8820 c d x + 3780 c d x + 945 c d x + 105 c d * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 945 d |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^6, x) (134) +----------+ | b log(F) d |- -------- | 2 4 4 +---+ a log(F) \| d - 8 b log(F) \|%pi %e erf(--------------) d x + c + 3 2 3 3 (8 b d x + 8 b c d)log(F) + 2 4 3 2 3 2 2 2 2 2 3 2 (4 b d x + 12 b c d x + 12 b c d x + 4 b c d)log(F) + 6 5 5 4 2 4 3 3 3 2 4 2 6 b d x + 30 b c d x + 60 b c d x + 60 b c d x + 30 b c d x + 5 6 b c d * log(F) + 8 7 7 6 2 6 5 3 5 4 4 4 3 15 d x + 105 c d x + 315 c d x + 525 c d x + 525 c d x + 5 3 2 6 2 7 315 c d x + 105 c d x + 15 c d * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 105 d |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^4, x) (135) +----------+ | b log(F) d |- -------- | 2 3 3 +---+ a log(F) \| d - 4 b log(F) \|%pi %e erf(--------------) d x + c + 2 2 2 2 (4 b d x + 4 b c d)log(F) + 4 3 3 2 2 2 3 6 5 (2 b d x + 6 b c d x + 6 b c d x + 2 b c d)log(F) + 3 d x + 5 4 2 4 3 3 3 2 4 2 5 15 c d x + 30 c d x + 30 c d x + 15 c d x + 3 c d * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 15 d |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)*(c+d*x)^2, x) (136) +----------+ | b log(F) d |- -------- | 2 2 2 +---+ a log(F) \| d - 2 b log(F) \|%pi %e erf(--------------) d x + c + 2 4 3 3 2 2 2 3 ((2 b d x + 2 b c d)log(F) + d x + 3 c d x + 3 c d x + c d) * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 | b log(F) 3 d |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^2), x) (137) +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d - b log(F)\|%pi %e erf(--------------) d x + c + 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ 2 d x + 2 c d x + c | b log(F) (d x + c d)%e |- -------- | 2 \| d / +----------+ 2 | b log(F) d |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^2, x) +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d \|%pi %e erf(--------------) d x + c (138) - ----------------------------------- +----------+ 2 | b log(F) 2 d |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^4, x) (139) +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d (d x + c)\|%pi %e erf(--------------) d x + c + 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) - 2 d %e |- -------- | 2 \| d / +----------+ 3 2 | b log(F) (4 b d x + 4 b c d )log(F) |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^6, x) (140) +----------+ | b log(F) d |- -------- | 2 3 3 2 2 2 3 +---+ a log(F) \| d (- 3 d x - 9 c d x - 9 c d x - 3 c )\|%pi %e erf(--------------) d x + c + 3 2 2 2 (- 4 b d log(F) + 6 d x + 12 c d x + 6 c d) * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / +----------+ 2 5 3 2 4 2 2 2 3 2 3 2 2 | b log(F) (8 b d x + 24 b c d x + 24 b c d x + 8 b c d )log(F) |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^8, x) (141) 5 5 4 4 2 3 3 3 2 2 4 5 (15 d x + 75 c d x + 150 c d x + 150 c d x + 75 c d x + 15 c ) * +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d \|%pi %e erf(--------------) d x + c + 2 2 3 2 2 2 5 4 - 8 b d log(F) + (20 b d x + 40 b c d x + 20 b c d)log(F) - 30 d x + 4 3 2 3 2 3 2 4 - 120 c d x - 180 c d x - 120 c d x - 30 c d * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / 3 7 5 3 6 4 3 2 5 3 3 3 4 2 3 4 3 16 b d x + 80 b c d x + 160 b c d x + 160 b c d x + 80 b c d x + 3 5 2 16 b c d * +----------+ 3 | b log(F) log(F) |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^10, x) (142) 7 7 6 6 2 5 5 3 4 4 4 3 3 - 105 d x - 735 c d x - 2205 c d x - 3675 c d x - 3675 c d x + 5 2 2 6 7 - 2205 c d x - 735 c d x - 105 c * +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d \|%pi %e erf(--------------) d x + c + 3 3 2 3 2 2 2 2 2 2 - 16 b d log(F) + (56 b d x + 112 b c d x + 56 b c d)log(F) + 5 4 4 3 2 3 2 3 2 - 140 b d x - 560 b c d x - 840 b c d x - 560 b c d x + 4 - 140 b c d * log(F) + 7 6 6 5 2 5 4 3 4 3 4 3 2 210 d x + 1260 c d x + 3150 c d x + 4200 c d x + 3150 c d x + 5 2 6 1260 c d x + 210 c d * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / 4 9 7 4 8 6 4 2 7 5 4 3 6 4 4 4 5 3 32 b d x + 224 b c d x + 672 b c d x + 1120 b c d x + 1120 b c d x + 4 5 4 2 4 6 3 4 7 2 672 b c d x + 224 b c d x + 32 b c d * +----------+ 4 | b log(F) log(F) |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.04 (EV) = 0.04 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^12, x) (143) 9 9 8 8 2 7 7 3 6 6 4 5 5 945 d x + 8505 c d x + 34020 c d x + 79380 c d x + 119070 c d x + 5 4 4 6 3 3 7 2 2 8 9 119070 c d x + 79380 c d x + 34020 c d x + 8505 c d x + 945 c * +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d \|%pi %e erf(--------------) d x + c + 4 4 3 3 2 3 2 3 2 3 - 32 b d log(F) + (144 b d x + 288 b c d x + 144 b c d)log(F) + 2 5 4 2 4 3 2 2 3 2 2 3 2 - 504 b d x - 2016 b c d x - 3024 b c d x - 2016 b c d x + 2 4 - 504 b c d * 2 log(F) + 7 6 6 5 2 5 4 3 4 3 1260 b d x + 7560 b c d x + 18900 b c d x + 25200 b c d x + 4 3 2 5 2 6 18900 b c d x + 7560 b c d x + 1260 b c d * log(F) + 9 8 8 7 2 7 6 3 6 5 - 1890 d x - 15120 c d x - 52920 c d x - 105840 c d x + 4 5 4 5 4 3 6 3 2 7 2 8 - 132300 c d x - 105840 c d x - 52920 c d x - 15120 c d x - 1890 c d * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / 5 11 9 5 10 8 5 2 9 7 5 3 8 6 64 b d x + 576 b c d x + 2304 b c d x + 5376 b c d x + 5 4 7 5 5 5 6 4 5 6 5 3 5 7 4 2 8064 b c d x + 8064 b c d x + 5376 b c d x + 2304 b c d x + 5 8 3 5 9 2 576 b c d x + 64 b c d * +----------+ 5 | b log(F) log(F) |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.05 (EV) = 0.05 sec integrate(F^(a+b/(c+d*x)^2)/(c+d*x)^14, x) (144) 11 11 10 10 2 9 9 3 8 8 - 10395 d x - 114345 c d x - 571725 c d x - 1715175 c d x + 4 7 7 5 6 6 6 5 5 7 4 4 - 3430350 c d x - 4802490 c d x - 4802490 c d x - 3430350 c d x + 8 3 3 9 2 2 10 11 - 1715175 c d x - 571725 c d x - 114345 c d x - 10395 c * +----------+ | b log(F) d |- -------- | 2 +---+ a log(F) \| d \|%pi %e erf(--------------) d x + c + 5 5 4 3 2 4 2 4 2 4 - 64 b d log(F) + (352 b d x + 704 b c d x + 352 b c d)log(F) + 3 5 4 3 4 3 3 2 3 2 3 3 2 - 1584 b d x - 6336 b c d x - 9504 b c d x - 6336 b c d x + 3 4 - 1584 b c d * 3 log(F) + 2 7 6 2 6 5 2 2 5 4 2 3 4 3 5544 b d x + 33264 b c d x + 83160 b c d x + 110880 b c d x + 2 4 3 2 2 5 2 2 6 83160 b c d x + 33264 b c d x + 5544 b c d * 2 log(F) + 9 8 8 7 2 7 6 - 13860 b d x - 110880 b c d x - 388080 b c d x + 3 6 5 4 5 4 5 4 3 - 776160 b c d x - 970200 b c d x - 776160 b c d x + 6 3 2 7 2 8 - 388080 b c d x - 110880 b c d x - 13860 b c d * log(F) + 11 10 10 9 2 9 8 3 8 7 20790 d x + 207900 c d x + 935550 c d x + 2494800 c d x + 4 7 6 5 6 5 6 5 4 7 4 3 4365900 c d x + 5239080 c d x + 4365900 c d x + 2494800 c d x + 8 3 2 9 2 10 935550 c d x + 207900 c d x + 20790 c d * 2 2 2 (a d x + 2 a c d x + a c + b)log(F) ------------------------------------- 2 2 2 +----------+ d x + 2 c d x + c | b log(F) %e |- -------- | 2 \| d / 6 13 11 6 12 10 6 2 11 9 6 3 10 8 128 b d x + 1408 b c d x + 7040 b c d x + 21120 b c d x + 6 4 9 7 6 5 8 6 6 6 7 5 6 7 6 4 42240 b c d x + 59136 b c d x + 59136 b c d x + 42240 b c d x + 6 8 5 3 6 9 4 2 6 10 3 6 11 2 21120 b c d x + 7040 b c d x + 1408 b c d x + 128 b c d * +----------+ 6 | b log(F) log(F) |- -------- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.06 (EV) + 0.02 (OT) = 0.08 sec integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^m, x) 3 3 2 2 2 3 %A a d + 3 %A a c d + 3 %A a c d + a c + b --------------------------------------------- x 3 3 2 2 2 3 ++ %A d + 3 %A c d + 3 %A c d + c m (145) | F (%A d + c) d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^14, x) (146) 4 3 3 4 2 2 4 2 4 3 4 (b d x + 3 b c d x + 3 b c d x + b c )log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 3 4 2 2 b d x + 6 b c d x + 15 b c d x + 20 b c d x + 15 b c d x + 3 5 3 6 6 b c d x + b c * 3 log(F) + 2 9 9 2 8 8 2 2 7 7 2 3 6 6 2 b d x + 18 b c d x + 72 b c d x + 168 b c d x + 2 4 5 5 2 5 4 4 2 6 3 3 2 7 2 2 252 b c d x + 252 b c d x + 168 b c d x + 72 b c d x + 2 8 2 9 18 b c d x + 2 b c * 2 log(F) + 12 12 11 11 2 10 10 3 9 9 6 b d x + 72 b c d x + 396 b c d x + 1320 b c d x + 4 8 8 5 7 7 6 6 6 7 5 5 2970 b c d x + 4752 b c d x + 5544 b c d x + 4752 b c d x + 8 4 4 9 3 3 10 2 2 11 2970 b c d x + 1320 b c d x + 396 b c d x + 72 b c d x + 12 6 b c * log(F) + 15 15 14 14 2 13 13 3 12 12 24 d x + 360 c d x + 2520 c d x + 10920 c d x + 4 11 11 5 10 10 6 9 9 7 8 8 32760 c d x + 72072 c d x + 120120 c d x + 154440 c d x + 8 7 7 9 6 6 10 5 5 11 4 4 154440 c d x + 120120 c d x + 72072 c d x + 32760 c d x + 12 3 3 13 2 2 14 15 10920 c d x + 2520 c d x + 360 c d x + 24 c * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e + 5 5 b log(F) a log(F) - b log(F) Ei(------------------------------)%e 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / 360 d Type: Union(Expression(Integer),...) fricasTime: 0.03 (EV) + 0.01 (OT) = 0.04 sec integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^11, x) (147) 3 3 3 3 2 2 3 2 3 3 3 (b d x + 3 b c d x + 3 b c d x + b c )log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 2 4 2 2 b d x + 6 b c d x + 15 b c d x + 20 b c d x + 15 b c d x + 2 5 2 6 6 b c d x + b c * 2 log(F) + 9 9 8 8 2 7 7 3 6 6 2 b d x + 18 b c d x + 72 b c d x + 168 b c d x + 4 5 5 5 4 4 6 3 3 7 2 2 252 b c d x + 252 b c d x + 168 b c d x + 72 b c d x + 8 9 18 b c d x + 2 b c * log(F) + 12 12 11 11 2 10 10 3 9 9 4 8 8 6 d x + 72 c d x + 396 c d x + 1320 c d x + 2970 c d x + 5 7 7 6 6 6 7 5 5 8 4 4 9 3 3 4752 c d x + 5544 c d x + 4752 c d x + 2970 c d x + 1320 c d x + 10 2 2 11 12 396 c d x + 72 c d x + 6 c * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e + 4 4 b log(F) a log(F) - b log(F) Ei(------------------------------)%e 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / 72 d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^8, x) (148) 2 3 3 2 2 2 2 2 2 3 2 (b d x + 3 b c d x + 3 b c d x + b c )log(F) + 6 6 5 5 2 4 4 3 3 3 4 2 2 b d x + 6 b c d x + 15 b c d x + 20 b c d x + 15 b c d x + 5 6 6 b c d x + b c * log(F) + 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 2 d x + 18 c d x + 72 c d x + 168 c d x + 252 c d x + 252 c d x + 6 3 3 7 2 2 8 9 168 c d x + 72 c d x + 18 c d x + 2 c * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e + 3 3 b log(F) a log(F) - b log(F) Ei(------------------------------)%e 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / 18 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (IN) + 0.02 (EV) + 0.01 (OT) = 0.04 sec integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^5, x) (149) 3 3 2 2 2 3 6 6 5 5 (b d x + 3 b c d x + 3 b c d x + b c )log(F) + d x + 6 c d x + 2 4 4 3 3 3 4 2 2 5 6 15 c d x + 20 c d x + 15 c d x + 6 c d x + c * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e + 2 2 b log(F) a log(F) - b log(F) Ei(------------------------------)%e 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / 6 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^2, x) (150) 3 3 2 2 2 3 (d x + 3 c d x + 3 c d x + c ) * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e + b log(F) a log(F) - b log(F)Ei(------------------------------)%e 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / 3 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x), x) b log(F) a log(F) Ei(------------------------------)%e 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c (151) - -------------------------------------------- 3 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^4, x) 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e (152) - ---------------------------------------------------- 3 b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^7, x) (153) 3 3 2 2 2 3 (- b log(F) + d x + 3 c d x + 3 c d x + c ) * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e / 2 4 3 2 3 2 2 2 2 2 3 2 (3 b d x + 9 b c d x + 9 b c d x + 3 b c d)log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^10, x) (154) 2 2 3 3 2 2 2 3 - b log(F) + (2 b d x + 6 b c d x + 6 b c d x + 2 b c )log(F) + 6 6 5 5 2 4 4 3 3 3 4 2 2 5 - 2 d x - 12 c d x - 30 c d x - 40 c d x - 30 c d x - 12 c d x + 6 - 2 c * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e / 3 7 6 3 6 5 3 2 5 4 3 3 4 3 3 4 3 2 3 b d x + 18 b c d x + 45 b c d x + 60 b c d x + 45 b c d x + 3 5 2 3 6 18 b c d x + 3 b c d * 3 log(F) Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) + 0.01 (OT) = 0.03 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^13, x) (155) 3 3 2 3 3 2 2 2 2 2 2 3 2 - b log(F) + (3 b d x + 9 b c d x + 9 b c d x + 3 b c )log(F) + 6 6 5 5 2 4 4 3 3 3 4 2 2 - 6 b d x - 36 b c d x - 90 b c d x - 120 b c d x - 90 b c d x + 5 6 - 36 b c d x - 6 b c * log(F) + 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 d x + 54 c d x + 216 c d x + 504 c d x + 756 c d x + 756 c d x + 6 3 3 7 2 2 8 9 504 c d x + 216 c d x + 54 c d x + 6 c * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e / 4 10 9 4 9 8 4 2 8 7 4 3 7 6 4 4 6 5 3 b d x + 27 b c d x + 108 b c d x + 252 b c d x + 378 b c d x + 4 5 5 4 4 6 4 3 4 7 3 2 4 8 2 4 9 378 b c d x + 252 b c d x + 108 b c d x + 27 b c d x + 3 b c d * 4 log(F) Type: Union(Expression(Integer),...) fricasTime: 0.05 (EV) + 0.01 (OT) = 0.06 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^16, x) (156) 4 4 3 3 3 3 2 2 3 2 3 3 3 - b log(F) + (4 b d x + 12 b c d x + 12 b c d x + 4 b c )log(F) + 2 6 6 2 5 5 2 2 4 4 2 3 3 3 - 12 b d x - 72 b c d x - 180 b c d x - 240 b c d x + 2 4 2 2 2 5 2 6 - 180 b c d x - 72 b c d x - 12 b c * 2 log(F) + 9 9 8 8 2 7 7 3 6 6 24 b d x + 216 b c d x + 864 b c d x + 2016 b c d x + 4 5 5 5 4 4 6 3 3 7 2 2 3024 b c d x + 3024 b c d x + 2016 b c d x + 864 b c d x + 8 9 216 b c d x + 24 b c * log(F) + 12 12 11 11 2 10 10 3 9 9 4 8 8 - 24 d x - 288 c d x - 1584 c d x - 5280 c d x - 11880 c d x + 5 7 7 6 6 6 7 5 5 8 4 4 - 19008 c d x - 22176 c d x - 19008 c d x - 11880 c d x + 9 3 3 10 2 2 11 12 - 5280 c d x - 1584 c d x - 288 c d x - 24 c * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e / 5 13 12 5 12 11 5 2 11 10 5 3 10 9 3 b d x + 36 b c d x + 198 b c d x + 660 b c d x + 5 4 9 8 5 5 8 7 5 6 7 6 5 7 6 5 1485 b c d x + 2376 b c d x + 2772 b c d x + 2376 b c d x + 5 8 5 4 5 9 4 3 5 10 3 2 5 11 2 5 12 1485 b c d x + 660 b c d x + 198 b c d x + 36 b c d x + 3 b c d * 5 log(F) Type: Union(Expression(Integer),...) fricasTime: 0.10 (EV) + 0.01 (OT) = 0.11 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^19, x) (157) 5 5 4 3 3 4 2 2 4 2 4 3 4 - b log(F) + (5 b d x + 15 b c d x + 15 b c d x + 5 b c )log(F) + 3 6 6 3 5 5 3 2 4 4 3 3 3 3 - 20 b d x - 120 b c d x - 300 b c d x - 400 b c d x + 3 4 2 2 3 5 3 6 - 300 b c d x - 120 b c d x - 20 b c * 3 log(F) + 2 9 9 2 8 8 2 2 7 7 2 3 6 6 60 b d x + 540 b c d x + 2160 b c d x + 5040 b c d x + 2 4 5 5 2 5 4 4 2 6 3 3 2 7 2 2 7560 b c d x + 7560 b c d x + 5040 b c d x + 2160 b c d x + 2 8 2 9 540 b c d x + 60 b c * 2 log(F) + 12 12 11 11 2 10 10 3 9 9 - 120 b d x - 1440 b c d x - 7920 b c d x - 26400 b c d x + 4 8 8 5 7 7 6 6 6 - 59400 b c d x - 95040 b c d x - 110880 b c d x + 7 5 5 8 4 4 9 3 3 10 2 2 - 95040 b c d x - 59400 b c d x - 26400 b c d x - 7920 b c d x + 11 12 - 1440 b c d x - 120 b c * log(F) + 15 15 14 14 2 13 13 3 12 12 120 d x + 1800 c d x + 12600 c d x + 54600 c d x + 4 11 11 5 10 10 6 9 9 7 8 8 163800 c d x + 360360 c d x + 600600 c d x + 772200 c d x + 8 7 7 9 6 6 10 5 5 11 4 4 772200 c d x + 600600 c d x + 360360 c d x + 163800 c d x + 12 3 3 13 2 2 14 15 54600 c d x + 12600 c d x + 1800 c d x + 120 c * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e / 6 16 15 6 15 14 6 2 14 13 6 3 13 12 3 b d x + 45 b c d x + 315 b c d x + 1365 b c d x + 6 4 12 11 6 5 11 10 6 6 10 9 6 7 9 8 4095 b c d x + 9009 b c d x + 15015 b c d x + 19305 b c d x + 6 8 8 7 6 9 7 6 6 10 6 5 6 11 5 4 19305 b c d x + 15015 b c d x + 9009 b c d x + 4095 b c d x + 6 12 4 3 6 13 3 2 6 14 2 6 15 1365 b c d x + 315 b c d x + 45 b c d x + 3 b c d * 6 log(F) Type: Union(Expression(Integer),...) fricasTime: 0.17 (EV) = 0.17 sec integrate(F^(a+b/(c+d*x)^3)*(c+d*x)^3, x) (158) 3 2 6 4 5 3 2 4 2 3 3 (3 b d x + 3 b c d )log(F) + d x + 4 c d x + 6 c d x + 4 c d x + 4 2 c d * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 +----------+2 d x + 3 c d x + 3 c d x + c | b log(F) %e |- -------- 3| 3 \| d + 2 2 a log(F) 2 b log(F) 3 b log(F) %e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / +----------+2 3 | b log(F) 4 d |- -------- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^3)*(c+d*x), x) (159) 3 2 2 2 (d x + 2 c d x + c d) * 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 +----------+ d x + 3 c d x + 3 c d x + c | b log(F) %e |- -------- 3| 3 \| d + a log(F) 1 b log(F) b log(F)%e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / +----------+ 2 | b log(F) 2 d |- -------- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^3), x) (160) 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 3 2 d x + 3 c d x + 3 c d x + c (d x + c d )%e * +----------+2 | b log(F) |- -------- 3| 3 \| d + a log(F) 2 b log(F) b log(F)%e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / +----------+2 3 | b log(F) d |- -------- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^2, x) a log(F) 1 b log(F) %e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c (161) --------------------------------------------------- +----------+ 2 | b log(F) 3 d |- -------- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^3, x) a log(F) 2 b log(F) %e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c (162) --------------------------------------------------- +----------+2 3 | b log(F) 3 d |- -------- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(F^(a+b/(c+d*x)^3)/(c+d*x)^5, x) (163) 3 3 2 2 2 3 (a d x + 3 a c d x + 3 a c d x + a c + b)log(F) -------------------------------------------------- 3 3 2 2 2 3 +----------+ d x + 3 c d x + 3 c d x + c | b log(F) - 3 d %e |- -------- 3| 3 \| d + a log(F) 1 b log(F) (- d x - c)%e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / +----------+ 3 2 | b log(F) (9 b d x + 9 b c d )log(F) |- -------- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec -- n symbolic integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^m, x) x n ++ m b (%A d + c) + a (164) | (%A d + c) F d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^3, x) x n ++ 3 3 2 2 2 3 b (%A d + c) + a (165) | (%A d + 3 %A c d + 3 %A c d + c )F d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^2, x) x n ++ 2 2 2 b (%A d + c) + a (166) | (%A d + 2 %A c d + c )F d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x), x) x n ++ b (%A d + c) + a (167) | (%A d + c)F d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^n), x) x n ++ b (%A d + c) + a (168) | F d%A ++ Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^n)/(c+d*x), x) a log(F) n log(d x + c) %e Ei(b log(F)%e ) (169) -------------------------------------- d n Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^2, x) n x b (%A d + c) + a ++ F (170) | --------------------- d%A ++ 2 2 2 %A d + 2 %A c d + c Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^3, x) n x b (%A d + c) + a ++ F (171) | --------------------------------- d%A ++ 3 3 2 2 2 3 %A d + 3 %A c d + 3 %A c d + c Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^n)/(c+d*x)^4, x) n x b (%A d + c) + a ++ F (172) | --------------------------------------------- d%A ++ 4 4 3 3 2 2 2 3 4 %A d + 4 %A c d + 6 %A c d + 4 %A c d + c Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+6*n), x) (173) 5 5 n log(d x + c) 5 4 4 n log(d x + c) 4 b log(F) (%e ) - 5 b log(F) (%e ) + 3 3 n log(d x + c) 3 2 2 n log(d x + c) 2 20 b log(F) (%e ) - 60 b log(F) (%e ) + n log(d x + c) 120 b log(F)%e - 120 * n log(d x + c) b log(F)%e + a log(F) %e / 6 6 b d n log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+5*n), x) (174) 4 4 n log(d x + c) 4 3 3 n log(d x + c) 3 b log(F) (%e ) - 4 b log(F) (%e ) + 2 2 n log(d x + c) 2 n log(d x + c) 12 b log(F) (%e ) - 24 b log(F)%e + 24 * n log(d x + c) b log(F)%e + a log(F) %e / 5 5 b d n log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+4*n), x) (175) 3 3 n log(d x + c) 3 2 2 n log(d x + c) 2 b log(F) (%e ) - 3 b log(F) (%e ) + n log(d x + c) 6 b log(F)%e - 6 * n log(d x + c) b log(F)%e + a log(F) %e / 4 4 b d n log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+3*n), x) (176) 2 2 n log(d x + c) 2 n log(d x + c) (b log(F) (%e ) - 2 b log(F)%e + 2) * n log(d x + c) b log(F)%e + a log(F) %e / 3 3 b d n log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+2*n), x) n log(d x + c) n log(d x + c) b log(F)%e + a log(F) (b log(F)%e - 1)%e (177) ------------------------------------------------------------------- 2 2 b d n log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1+n), x) n log(d x + c) b log(F)%e + a log(F) %e (178) ------------------------------------- b d n log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^n)/(c+d*x), x) a log(F) n log(d x + c) %e Ei(b log(F)%e ) (179) -------------------------------------- d n Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-n), x) (180) n log(d x + c) b log(F)%e + a log(F) - %e + a log(F) n log(d x + c) n log(d x + c) b log(F)%e %e Ei(b log(F)%e ) / n log(d x + c) d n %e Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-2*n), x) (181) n log(d x + c) n log(d x + c) b log(F)%e + a log(F) (- b log(F)%e - 1)%e + 2 2 a log(F) n log(d x + c) 2 n log(d x + c) b log(F) %e (%e ) Ei(b log(F)%e ) / n log(d x + c) 2 2 d n (%e ) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-3*n), x) (182) 2 2 n log(d x + c) 2 n log(d x + c) (- b log(F) (%e ) - b log(F)%e - 2) * n log(d x + c) b log(F)%e + a log(F) %e + 3 3 a log(F) n log(d x + c) 3 n log(d x + c) b log(F) %e (%e ) Ei(b log(F)%e ) / n log(d x + c) 3 6 d n (%e ) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-4*n), x) (183) 3 3 n log(d x + c) 3 2 2 n log(d x + c) 2 - b log(F) (%e ) - b log(F) (%e ) + n log(d x + c) - 2 b log(F)%e - 6 * n log(d x + c) b log(F)%e + a log(F) %e + 4 4 a log(F) n log(d x + c) 4 n log(d x + c) b log(F) %e (%e ) Ei(b log(F)%e ) / n log(d x + c) 4 24 d n (%e ) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^n)*(c+d*x)^(-1-5*n), x) (184) 4 4 n log(d x + c) 4 3 3 n log(d x + c) 3 - b log(F) (%e ) - b log(F) (%e ) + 2 2 n log(d x + c) 2 n log(d x + c) - 2 b log(F) (%e ) - 6 b log(F)%e - 24 * n log(d x + c) b log(F)%e + a log(F) %e + 5 5 a log(F) n log(d x + c) 5 n log(d x + c) b log(F) %e (%e ) Ei(b log(F)%e ) / n log(d x + c) 5 120 d n (%e ) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(c*(a+b*x)^n)*(a+b*x)^(-1+1/2*n), x) (n - 2)log(b x + a) ------------------- +---+ 2 +----------+ \|%pi erf((b x + a)%e \|- c log(F) ) (185) ------------------------------------------------------ +----------+ b n\|- c log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (IN) + 0.01 (EV) + 0.01 (OT) = 0.03 sec integrate((a+b*x)^(-1+1/2*n)/F^(c*(a+b*x)^n), x) (n - 2)log(b x + a) ------------------- +---+ 2 +--------+ \|%pi erf((b x + a)%e \|c log(F) ) (186) ---------------------------------------------------- +--------+ b n\|c log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec -- Integrands of the form (e+f x)^m F^(a+b (c+d x)^n) -- n>0 integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^5, x) (187) 3 5 5 3 4 2 4 3 3 3 2 3 3 2 4 3 2 - 4 b c d f + 20 b c d e f - 40 b c d e f + 40 b c d e f + 3 5 4 3 6 5 - 20 b c d e f + 4 b d e * 3 log(F) + 2 3 5 2 2 2 4 2 3 2 3 2 4 3 2 2 (20 b c d f - 60 b c d e f + 60 b c d e f - 20 b d e f )log(F) + 5 2 4 (- 15 b c d f + 15 b d e f )log(F) * +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d + 2 4 5 4 2 3 5 2 4 4 3 4 b d f x + (- 4 b c d f + 20 b d e f )x + 2 2 2 5 2 3 4 2 4 2 3 2 (4 b c d f - 20 b c d e f + 40 b d e f )x + 2 3 5 2 2 2 4 2 3 2 3 2 4 3 2 (- 4 b c d f + 20 b c d e f - 40 b c d e f + 40 b d e f )x + 2 4 5 2 3 4 2 2 2 2 3 2 3 3 2 4 b c f - 20 b c d e f + 40 b c d e f - 40 b c d e f + 2 4 4 20 b d e f * 2 log(F) + 2 5 2 5 2 4 2 5 - 8 b d f x + (14 b c d f - 30 b d e f )x - 18 b c f + 4 2 2 3 50 b c d e f - 40 b d e f * log(F) + 5 8 f * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 3 6 3 | 2 8 b d log(F) \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) + 0.01 (OT) = 0.03 sec integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^4, x) (188) 2 4 4 2 3 2 3 2 2 3 2 2 2 4 3 4 b c d f - 16 b c d e f + 24 b c d e f - 16 b c d e f + 2 5 4 4 b d e * 2 log(F) + 2 4 2 3 3 2 2 4 (- 12 b c d f + 24 b c d e f - 12 b d e f )log(F) + 3 d f * +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d + 3 4 3 2 4 3 3 2 4 b d f x + (- 4 b c d f + 16 b d e f )x + 2 4 2 3 3 2 2 3 4 (4 b c d f - 16 b c d e f + 24 b d e f )x - 4 b c f + 2 3 2 2 2 3 3 16 b c d e f - 24 b c d e f + 16 b d e f * log(F) + 4 4 3 - 6 d f x + 10 c f - 16 d e f * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 2 5 2 | 2 8 b d log(F) \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^3, x) (189) 2 3 3 2 2 2 2 2 3 2 2 4 3 2 (- 2 b c d f + 6 b c d e f - 6 b c d e f + 2 b d e )log(F) + 3 2 2 (3 b c d f - 3 b d e f )log(F) * +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d + 2 3 2 3 2 2 2 3 2 b d f x + (- 2 b c d f + 6 b d e f )x + 2 b c f + 2 2 2 - 6 b c d e f + 6 b d e f * log(F) + 3 - 2 f * 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 %e \|- b d log(F) / +------------+ 2 4 2 | 2 4 b d log(F) \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^2)*(e+f*x)^2, x) (190) 2 2 2 3 2 2 +---+ a log(F) ((2 b c d f - 4 b c d e f + 2 b d e )log(F) - d f )\|%pi %e * +------------+ | 2 (d x + c)\|- b d log(F) erf(------------------------) d + 2 2 2 2 2 (b d x + 2 b c d x + b c + a)log(F) (2 d f x - 2 c f + 4 d e f)%e * +------------+ | 2 \|- b d log(F) / +------------+ 3 | 2 4 b d log(F)\|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b*(c+d*x)^2)*(e+f*x), x) (191) +------------+ | 2 2 +---+ a log(F) (d x + c)\|- b d log(F) (- b c d f + b d e)log(F)\|%pi %e erf(------------------------) d + 2 2 2 +------------+ (b d x + 2 b c d x + b c + a)log(F) | 2 f %e \|- b d log(F) / +------------+ 2 | 2 2 b d log(F)\|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2), x) +------------+ | 2 +---+ a log(F) (d x + c)\|- b d log(F) \|%pi %e erf(------------------------) d (192) --------------------------------------------- +------------+ | 2 2 \|- b d log(F) Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)/(e+f*x), x) 2 2 2 x %A b d + 2 %A b c d + b c + a ++ F (193) | -------------------------------- d%A ++ %A f + e Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(F^(a+b*(c+d*x)^2)/(e+f*x)^2, x) 2 2 2 x %A b d + 2 %A b c d + b c + a ++ F (194) | -------------------------------- d%A ++ 2 2 2 %A f + 2 %A e f + e Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b*(c+d*x)^2)/(e+f*x)^3, x) 2 2 2 x %A b d + 2 %A b c d + b c + a ++ F (195) | --------------------------------- d%A ++ 3 3 2 2 2 3 %A f + 3 %A e f + 3 %A e f + e Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(%e^(e*(c+d*x)^3)*(a+b*x)^3, x) (196) 3 3 2 2 2 3 3 2 3 d e x + 3 c d e x + 3 c d e x + c e (3 b d x + 9 a b d - 6 b c)%e * +-----+2 3| 3 \|- d e + 3 4 2 3 2 2 2 3 3 3 ((- 3 a d + 9 a b c d - 9 a b c d + 3 b c d)e + b d) * +-----+ 1 3 3 2 2 2 3 3| 3 Gamma(-,- d e x - 3 c d e x - 3 c d e x - c e)\|- d e 3 + 2 4 2 3 3 2 2 (- 9 a b d + 18 a b c d - 9 b c d )e * 2 3 3 2 2 2 3 Gamma(-,- d e x - 3 c d e x - 3 c d e x - c e) 3 / +-----+2 4 3| 3 9 d e \|- d e Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(e*(c+d*x)^3)*(a+b*x)^2, x) (197) 3 3 2 2 2 3 +-----+2 2 d e x + 3 c d e x + 3 c d e x + c e 3| 3 b %e \|- d e + 2 3 2 2 2 (- a d + 2 a b c d - b c d)e * +-----+ 1 3 3 2 2 2 3 3| 3 Gamma(-,- d e x - 3 c d e x - 3 c d e x - c e)\|- d e 3 + 3 2 2 2 3 3 2 2 2 3 (- 2 a b d + 2 b c d )e Gamma(-,- d e x - 3 c d e x - 3 c d e x - c e) 3 / +-----+2 3 3| 3 3 d e \|- d e Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e*(c+d*x)^3)*(a+b*x), x) (198) +-----+ 1 3 3 2 2 2 3 3| 3 (- a d + b c)Gamma(-,- d e x - 3 c d e x - 3 c d e x - c e)\|- d e 3 + 2 3 3 2 2 2 3 - b d Gamma(-,- d e x - 3 c d e x - 3 c d e x - c e) 3 / +-----+2 3| 3 3 d \|- d e Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(e*(c+d*x)^3), x) 1 3 3 2 2 2 3 Gamma(-,- d e x - 3 c d e x - 3 c d e x - c e) 3 (199) - ------------------------------------------------ +-----+ 3| 3 3 \|- d e Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e*(c+d*x)^3)/(a+b*x), x) 3 3 2 2 2 3 x (%A d + 3 %A c d + 3 %A c d + c )e ++ %e (200) | -------------------------------------- d%A ++ %A b + a Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(e*(c+d*x)^3)/(a+b*x)^2, x) 3 3 2 2 2 3 x (%A d + 3 %A c d + 3 %A c d + c )e ++ %e (201) | -------------------------------------- d%A ++ 2 2 2 %A b + 2 %A a b + a Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec -- n<0 integrate(F^(a+b/(c+d*x))/(e+f*x), x) (202) ((a c + b)f - a d e)log(F) -------------------------- (- b d f x - b d e)log(F) c f - d e Ei(----------------------------)%e 2 2 (c d f - d e)x + c f - c d e + b log(F) a log(F) - Ei(--------)%e d x + c / f Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(F^(a+b/(c+d*x))/(e+f*x)^2, x) (203) (- b d f x - b d e)log(F) (- b d f x - b d e)log(F)Ei(----------------------------) 2 2 (c d f - d e)x + c f - c d e * ((a c + b)f - a d e)log(F) -------------------------- c f - d e %e + (a d x + a c + b)log(F) ----------------------- 2 2 d x + c ((- c d f + d e)x - c f + c d e)%e / 2 3 2 2 2 2 2 2 2 3 (c f - 2 c d e f + d e f)x + c e f - 2 c d e f + d e Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(F^(a+b/(c+d*x))/(e+f*x)^3, x) (204) 2 2 3 2 2 2 2 2 2 2 2 (b d f x + 2 b d e f x + b d e f)log(F) + 2 3 3 2 2 2 2 3 2 (2 b c d f - 2 b d e f )x + (4 b c d e f - 4 b d e f)x + 2 2 3 3 2 b c d e f - 2 b d e * log(F) * ((a c + b)f - a d e)log(F) -------------------------- (- b d f x - b d e)log(F) c f - d e Ei(----------------------------)%e 2 2 (c d f - d e)x + c f - c d e + 2 3 3 2 2 2 3 3 2 2 2 (b c d f - b d e f )x + (b c d f - b d e f)x + b c d e f + 2 2 - b c d e f * log(F) + 2 2 3 3 2 4 2 2 2 2 2 3 2 4 3 (c d f - 2 c d e f + d e f)x + (2 c d e f - 4 c d e f + 2 d e )x + 4 3 3 2 2 2 2 3 3 - c f + 4 c d e f - 5 c d e f + 2 c d e * (a d x + a c + b)log(F) ----------------------- d x + c %e / 4 6 3 5 2 2 2 4 3 3 3 4 4 2 2 (2 c f - 8 c d e f + 12 c d e f - 8 c d e f + 2 d e f )x + 4 5 3 2 4 2 2 3 3 3 4 2 4 5 (4 c e f - 16 c d e f + 24 c d e f - 16 c d e f + 4 d e f)x + 4 2 4 3 3 3 2 2 4 2 3 5 4 6 2 c e f - 8 c d e f + 12 c d e f - 8 c d e f + 2 d e Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) + 0.01 (OT) = 0.03 sec integrate(F^(a+b/(c+d*x))/(e+f*x)^4, x) (205) 3 3 5 3 3 3 4 2 3 3 2 3 3 3 3 2 3 (- b d f x - 3 b d e f x - 3 b d e f x - b d e f )log(F) + 2 3 5 2 4 4 3 2 3 4 2 4 2 3 2 (- 6 b c d f + 6 b d e f )x + (- 18 b c d e f + 18 b d e f )x + 2 3 2 3 2 4 3 2 2 3 3 2 2 4 4 (- 18 b c d e f + 18 b d e f )x - 6 b c d e f + 6 b d e f * 2 log(F) + 2 3 5 4 4 5 2 3 3 (- 6 b c d f + 12 b c d e f - 6 b d e f )x + 2 3 4 4 2 3 5 3 2 2 (- 18 b c d e f + 36 b c d e f - 18 b d e f )x + 2 3 2 3 4 3 2 5 4 2 3 3 2 (- 18 b c d e f + 36 b c d e f - 18 b d e f)x - 6 b c d e f + 4 4 5 5 12 b c d e f - 6 b d e * log(F) * ((a c + b)f - a d e)log(F) -------------------------- (- b d f x - b d e)log(F) c f - d e Ei(----------------------------)%e 2 2 (c d f - d e)x + c f - c d e + 2 3 5 2 4 4 3 (- b c d f + b d e f )x + 2 2 2 5 2 3 4 2 4 2 3 2 (- b c d f - b c d e f + 2 b d e f )x + 2 2 2 4 2 3 2 3 2 4 3 2 2 2 2 2 3 2 3 3 2 (- 2 b c d e f + b c d e f + b d e f )x - b c d e f + b c d e f * 2 log(F) + 2 3 5 4 4 5 2 3 3 (- 5 b c d f + 10 b c d e f - 5 b d e f )x + 3 2 5 2 3 4 4 2 3 5 3 2 2 (- 4 b c d f - 3 b c d e f + 18 b c d e f - 11 b d e f )x + 4 5 3 2 4 2 3 2 3 4 3 2 b c d f - 12 b c d e f + 15 b c d e f + 2 b c d e f + 5 4 - 6 b d e f * x + 4 4 3 2 2 3 2 3 3 2 4 4 b c d e f - 8 b c d e f + 13 b c d e f - 6 b c d e f * log(F) + 3 3 5 2 4 4 5 2 3 6 3 2 3 (- 2 c d f + 6 c d e f - 6 c d e f + 2 d e f )x + 3 3 4 2 4 2 3 5 3 2 6 4 2 (- 6 c d e f + 18 c d e f - 18 c d e f + 6 d e f)x + 3 3 2 3 2 4 3 2 5 4 6 5 6 5 (- 6 c d e f + 18 c d e f - 18 c d e f + 6 d e )x - 2 c f + 5 4 4 2 2 3 3 3 3 2 2 4 4 5 5 12 c d e f - 30 c d e f + 38 c d e f - 24 c d e f + 6 c d e * (a d x + a c + b)log(F) ----------------------- d x + c %e / 6 9 5 8 4 2 2 7 3 3 3 6 2 4 4 5 6 c f - 36 c d e f + 90 c d e f - 120 c d e f + 90 c d e f + 5 5 4 6 6 3 - 36 c d e f + 6 d e f * 3 x + 6 8 5 2 7 4 2 3 6 3 3 4 5 2 4 5 4 18 c e f - 108 c d e f + 270 c d e f - 360 c d e f + 270 c d e f + 5 6 3 6 7 2 - 108 c d e f + 18 d e f * 2 x + 6 2 7 5 3 6 4 2 4 5 3 3 5 4 2 4 6 3 18 c e f - 108 c d e f + 270 c d e f - 360 c d e f + 270 c d e f + 5 7 2 6 8 - 108 c d e f + 18 d e f * x + 6 3 6 5 4 5 4 2 5 4 3 3 6 3 2 4 7 2 6 c e f - 36 c d e f + 90 c d e f - 120 c d e f + 90 c d e f + 5 8 6 9 - 36 c d e f + 6 d e Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) + 0.02 (OT) = 0.04 sec integrate(%e^(e/(c+d*x))*(a+b*x)^4, x) (206) 4 5 5 4 4 3 5 4 24 b d x + (6 b d e + 120 a b d )x + 4 3 2 3 4 4 3 2 2 5 3 (2 b d e + (40 a b d - 16 b c d )e + 240 a b d )x + 4 2 3 3 3 4 2 2 b d e + (20 a b d - 14 b c d )e + 2 2 4 3 3 4 2 2 3 5 (120 a b d - 120 a b c d + 36 b c d )e + 240 a b d * 2 x + 4 4 3 2 4 3 b d e + (20 a b d - 18 b c d)e + 2 2 3 3 2 4 2 2 (120 a b d - 200 a b c d + 86 b c d)e + 3 4 2 2 3 3 2 2 4 3 4 5 (240 a b d - 480 a b c d + 360 a b c d - 96 b c d)e + 120 a d * x + 4 4 3 4 2 3 b c e + (20 a b c d - 19 b c )e + 2 2 2 3 2 4 3 2 (120 a b c d - 220 a b c d + 102 b c )e + 3 3 2 2 2 2 3 3 4 4 4 4 (240 a b c d - 600 a b c d + 520 a b c d - 154 b c )e + 120 a c d + 3 2 3 2 2 3 2 3 4 4 5 - 240 a b c d + 240 a b c d - 120 a b c d + 24 b c * e ------- d x + c %e + 4 5 3 4 4 - b e + (- 20 a b d + 20 b c)e + 2 2 2 3 4 2 3 (- 120 a b d + 240 a b c d - 120 b c )e + 3 3 2 2 2 3 2 4 3 2 (- 240 a b d + 720 a b c d - 720 a b c d + 240 b c )e + 4 4 3 3 2 2 2 2 3 3 4 4 (- 120 a d + 480 a b c d - 720 a b c d + 480 a b c d - 120 b c )e * e Ei(-------) d x + c / 5 120 d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(%e^(e/(c+d*x))*(a+b*x)^3, x) (207) 3 4 4 3 3 2 4 3 6 b d x + (2 b d e + 24 a b d )x + 3 2 2 2 3 3 2 2 4 2 (b d e + (12 a b d - 6 b c d )e + 36 a b d )x + 3 3 2 2 3 2 b d e + (12 a b d - 10 b c d)e + 2 3 2 2 3 2 3 4 (36 a b d - 48 a b c d + 18 b c d)e + 24 a d * x + 3 3 2 3 2 2 b c e + (12 a b c d - 11 b c )e + 2 2 2 2 3 3 3 3 2 2 2 (36 a b c d - 60 a b c d + 26 b c )e + 24 a c d - 36 a b c d + 2 3 3 4 24 a b c d - 6 b c * e ------- d x + c %e + 3 4 2 3 3 - b e + (- 12 a b d + 12 b c)e + 2 2 2 3 2 2 (- 36 a b d + 72 a b c d - 36 b c )e + 3 3 2 2 2 2 3 3 (- 24 a d + 72 a b c d - 72 a b c d + 24 b c )e * e Ei(-------) d x + c / 4 24 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(%e^(e/(c+d*x))*(a+b*x)^2, x) (208) 2 3 3 2 2 3 2 2 b d x + (b d e + 6 a b d )x + 2 2 2 2 2 3 2 2 (b d e + (6 a b d - 4 b c d)e + 6 a d )x + b c e + 2 2 2 2 2 2 3 (6 a b c d - 5 b c )e + 6 a c d - 6 a b c d + 2 b c * e ------- d x + c %e + 2 3 2 2 2 2 2 2 (- b e + (- 6 a b d + 6 b c)e + (- 6 a d + 12 a b c d - 6 b c )e) * e Ei(-------) d x + c / 3 6 d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(e/(c+d*x))*(a+b*x), x) (209) e ------- 2 2 2 2 d x + c (b d x + (b d e + 2 a d )x + b c e + 2 a c d - b c )%e + 2 e (- b e + (- 2 a d + 2 b c)e)Ei(-------) d x + c / 2 2 d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e/(c+d*x)), x) e ------- d x + c e (d x + c)%e - e Ei(-------) d x + c (210) ---------------------------------- d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(e/(c+d*x))/(a+b*x), x) b e - --------- b d e x + a d e a d - b c e Ei(------------------------------)%e - Ei(-------) 2 2 d x + c (a d - b c d)x + a c d - b c (211) ------------------------------------------------------------- b Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e/(c+d*x))/(a+b*x)^2, x) (212) e ------- 2 2 d x + c ((a d - b c d)x + a c d - b c )%e + b e - --------- b d e x + a d e a d - b c (- b d e x - a d e)Ei(------------------------------)%e 2 2 (a d - b c d)x + a c d - b c / 2 2 2 3 2 3 2 2 2 2 (a b d - 2 a b c d + b c )x + a d - 2 a b c d + a b c Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e/(c+d*x))/(a+b*x)^3, x) (213) 2 3 3 2 2 4 2 3 3 2 2 2 ((- a b d + b c d )e + a b d - 2 a b c d + b c d )x + 2 3 3 2 3 4 2 3 2 2 2 ((- a b d + b c d)e + 2 a d - 4 a b c d + 2 a b c d )x + 2 2 2 2 3 3 2 2 2 2 3 3 4 (- a b c d + a b c d)e + 2 a c d - 5 a b c d + 4 a b c d - b c * e ------- d x + c %e + 3 2 2 2 3 3 2 2 (b d e + (- 2 a b d + 2 b c d )e)x + 2 2 2 2 3 2 2 2 2 2 (2 a b d e + (- 4 a b d + 4 a b c d )e)x + a b d e + 3 3 2 2 (- 2 a d + 2 a b c d )e * b e - --------- b d e x + a d e a d - b c Ei(------------------------------)%e 2 2 (a d - b c d)x + a c d - b c / 4 2 4 3 3 3 2 4 2 2 5 3 6 4 2 (2 a b d - 8 a b c d + 12 a b c d - 8 a b c d + 2 b c )x + 5 4 4 2 3 3 3 2 2 2 4 3 5 4 6 4 (4 a b d - 16 a b c d + 24 a b c d - 16 a b c d + 4 a b c )x + 2 a d + 5 3 4 2 2 2 3 3 3 2 4 4 - 8 a b c d + 12 a b c d - 8 a b c d + 2 a b c Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(%e^(e/(c+d*x)^2)*(a+b*x)^3, x) (214) 2 3 2 (- 8 a b d + 8 b c)e + 3 3 2 2 2 2 3 3 (- 4 a d + 12 a b c d - 12 a b c d + 4 b c )e * +----+ | e d |- -- | 2 +---+ \| d \|%pi erf(--------) d x + c + 3 5 4 2 5 3 3 3 2 5 2 b d x + 4 a b d x + (b d e + 6 a b d )x + 2 3 3 2 3 5 2 2 3 2 ((8 a b d - 6 b c d )e + 4 a d )x + (8 a b c d - 7 b c d)e + 3 4 2 2 3 2 3 2 3 4 4 a c d - 6 a b c d + 4 a b c d - b c d * e ------------------- 2 2 2 d x + 2 c d x + c %e + 3 2 2 3 2 2 3 2 (- b d e + (- 6 a b d + 12 a b c d - 6 b c d)e) * e Ei(-------------------) 2 2 2 d x + 2 c d x + c * +----+ | e |- -- | 2 \| d / +----+ 5 | e 4 d |- -- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) + 0.01 (OT) = 0.02 sec integrate(%e^(e/(c+d*x)^2)*(a+b*x)^2, x) (215) +----+ | e d |- -- | 2 2 2 2 2 2 2 +---+ \| d (- 2 b e + (- 3 a d + 6 a b c d - 3 b c )e)\|%pi erf(--------) d x + c + 2 4 3 4 2 2 2 2 4 2 2 3 b d x + 3 a b d x + (2 b d e + 3 a d )x + 2 b c d e + 3 a c d + 2 2 2 3 - 3 a b c d + b c d * e ------------------- 2 2 2 d x + 2 c d x + c %e + 2 2 e (- 3 a b d + 3 b c d)e Ei(-------------------) 2 2 2 d x + 2 c d x + c * +----+ | e |- -- | 2 \| d / +----+ 4 | e 3 d |- -- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e/(c+d*x)^2)*(a+b*x), x) (216) +----+ | e d |- -- | 2 +---+ \| d (- 2 a d + 2 b c)e\|%pi erf(--------) d x + c + e ------------------- 2 2 2 3 2 3 2 2 d x + 2 c d x + c (b d x + 2 a d x + 2 a c d - b c d)%e + e - b d e Ei(-------------------) 2 2 2 d x + 2 c d x + c * +----+ | e |- -- | 2 \| d / +----+ 3 | e 2 d |- -- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (OT) = 0.01 sec integrate(%e^(e/(c+d*x)^2), x) +----+ | e e d |- -- ------------------- | 2 2 2 2 +----+ +---+ \| d 2 d x + 2 c d x + c | e - e\|%pi erf(--------) + (d x + c d)%e |- -- d x + c | 2 \| d (217) ---------------------------------------------------------------- +----+ 2 | e d |- -- | 2 \| d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(e/(c+d*x)^2)/(a+b*x), x) e --------------------- 2 2 2 x %A d + 2 %A c d + c ++ %e (218) | ----------------------- d%A ++ %A b + a Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e/(c+d*x)^2)/(a+b*x)^2, x) e --------------------- 2 2 2 x %A d + 2 %A c d + c ++ %e (219) | ----------------------- d%A ++ 2 2 2 %A b + 2 %A a b + a Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(%e^(e/(c+d*x)^2)/(a+b*x)^3, x) e --------------------- 2 2 2 x %A d + 2 %A c d + c ++ %e (220) | --------------------------------- d%A ++ 3 3 2 2 2 3 %A b + 3 %A a b + 3 %A a b + a Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(%e^(e/(c+d*x)^3)*(a+b*x)^3, x) (221) 3 6 4 2 6 3 2 6 2 3 3 3 6 b d x + 4 a b d x + 6 a b d x + (3 b d e + 4 a d )x + 3 2 3 5 2 2 4 2 3 3 3 4 2 3 b c d e + 4 a c d - 6 a b c d + 4 a b c d - b c d * e ------------------------------ 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e + 2 3 3 2 e (- 4 a b d + 4 b c d )e Ei(------------------------------) 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c * +----+2 | e |- -- 3| 3 \| d + 2 3 2 2 3 2 (6 a b d - 12 a b c d + 6 b c d)e * +----+ 1 e | e Gamma(-,- ------------------------------) |- -- 3 3 3 2 2 2 3 3| 3 d x + 3 c d x + 3 c d x + c \| d + 3 2 3 3 2 2 2 2 3 3 (3 b e + (4 a d - 12 a b c d + 12 a b c d - 4 b c )e) * 2 e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / +----+2 6 | e 4 d |- -- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec integrate(%e^(e/(c+d*x)^3)*(a+b*x)^2, x) (222) 2 5 3 5 2 2 5 2 4 2 3 2 3 2 (b d x + 3 a b d x + 3 a d x + 3 a c d - 3 a b c d + b c d ) * e ------------------------------ 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c %e + 2 2 e - b d e Ei(------------------------------) 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c * +----+2 | e |- -- 3| 3 \| d + +----+ 2 2 1 e | e (3 a b d - 3 b c d)e Gamma(-,- ------------------------------) |- -- 3 3 3 2 2 2 3 3| 3 d x + 3 c d x + 3 c d x + c \| d + 2 2 2 2 2 e (3 a d - 6 a b c d + 3 b c )e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / +----+2 5 | e 3 d |- -- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e/(c+d*x)^3)*(a+b*x), x) (223) e ------------------------------ 3 3 2 2 2 3 4 2 4 3 2 2 d x + 3 c d x + 3 c d x + c (b d x + 2 a d x + 2 a c d - b c d )%e * +----+2 | e |- -- 3| 3 \| d + +----+ 1 e | e b d e Gamma(-,- ------------------------------) |- -- 3 3 3 2 2 2 3 3| 3 d x + 3 c d x + 3 c d x + c \| d + 2 e (2 a d - 2 b c)e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / +----+2 4 | e 2 d |- -- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0 sec integrate(%e^(e/(c+d*x)^3), x) (224) e ------------------------------ 3 3 2 2 2 3 +----+2 3 2 d x + 3 c d x + 3 c d x + c | e (d x + c d )%e |- -- 3| 3 \| d + 2 e e Gamma(-,- ------------------------------) 3 3 3 2 2 2 3 d x + 3 c d x + 3 c d x + c / +----+2 3 | e d |- -- 3| 3 \| d Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e/(c+d*x)^3)/(a+b*x), x) e --------------------------------- 3 3 2 2 2 3 x %A d + 3 %A c d + 3 %A c d + c ++ %e (225) | ----------------------------------- d%A ++ %A b + a Type: Union(Expression(Integer),...) fricasTime: 0.01 (EV) = 0.01 sec integrate(%e^(e/(c+d*x)^3)/(a+b*x)^2, x) e --------------------------------- 3 3 2 2 2 3 x %A d + 3 %A c d + 3 %A c d + c ++ %e (226) | ----------------------------------- d%A ++ 2 2 2 %A b + 2 %A a b + a Type: Union(Expression(Integer),...) fricasTime: 0.02 (EV) = 0.02 sec

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