MathAction #154 integrate does not produce asinh

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Why doesn't Axiom express antiderivatives in terms of hyperbolic trig functions since in can differentiate such functions? For example:

fricas

(1) -> integrate(1/sqrt(1+x^2),x)

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

(1)

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

fricas

simplifyLog(%)

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

(2)

Type: Expression(Integer)

fricas

differentiate(%,x)

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

(3)

Type: Expression(Integer)

fricas

differentiate(asinh(x),x)

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

(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

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

Severity: normal => wishlist

Subject: Be Bold !!

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