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#154 integrate does not produce asinh

Edit detail for #154 integrate does not produce asinh revision 2 of 2

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Editor: test1 Time: 2014/04/23 19:24:36 GMT+0
Note:

added:

From test1 Wed Apr 23 19:24:36 +0000 2014
From: test1
Date: Wed, 23 Apr 2014 19:24:36 +0000
Subject: 
Message-ID: <20140423192436+0000@axiom-wiki.newsynthesis.org>

Severity: normal => wishlist

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