MathAction #154 integrate does not produce asinh

Topics

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)

$\label{eq1}-{\log \left({{\sqrt{{x^2}+ 1}}- x}\right)}$

Type: Union(Expression(Integer),...)

axiom

simplifyLog(%)

$\label{eq2}\log \left({1 \over{{\sqrt{{x^2}+ 1}}- x}}\right)$

Type: Expression(Integer)

axiom

differentiate(%,x)

$\label{eq3}{-{2 \ x \ {\sqrt{{x^2}+ 1}}}+{2 \ {x^2}}+ 1}\over{{{\left({2 \ {x^2}}+ 1 \right)}\ {\sqrt{{x^2}+ 1}}}-{2 \ {x^3}}-{2 \ x}}$

Type: Expression(Integer)

axiom

differentiate(asinh(x),x)

$\label{eq4}1 \over{\sqrt{{x^2}+ 1}}$

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

... --test1, Wed, 23 Apr 2014 19:24:36 +0000 reply

Severity: normal => wishlist