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Submitted by : (unknown) at: 2007-11-17T21:59:07-08:00 (9 years ago)
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Why doesn't Axiom express antiderivatives in terms of hyperbolic trig functions since in can differentiate such functions? For example:

axiom
integrate(1/sqrt(1+x^2),x)

\label{eq1}-{\log \left({{\sqrt{{x^2}+ 1}}- x}\right)}(1)
Type: Union(Expression(Integer),...)
axiom
simplifyLog(%)

\label{eq2}\log \left({1 \over{{\sqrt{{x^2}+ 1}}- x}}\right)(2)
Type: Expression(Integer)
axiom
differentiate(%,x)

\label{eq3}{-{2 \  x \ {\sqrt{{x^2}+ 1}}}+{2 \ {x^2}}+ 1}\over{{{\left({2 \ {x^2}}+ 1 \right)}\ {\sqrt{{x^2}+ 1}}}-{2 \ {x^3}}-{2 \  x}}(3)
Type: Expression(Integer)
axiom
differentiate(asinh(x),x)

\label{eq4}1 \over{\sqrt{{x^2}+ 1}}(4)
Type: Expression(Integer)

property change --kratt6, Mon, 03 Jul 2006 15:19:53 -0500 reply
Category: MathAction => Axiom Library Severity: minor => normal Status: pending (next release) => open

Severity: normal => wishlist




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