#11233: failing calculation of an integral
-------------------------+--------------------------------------------------
Reporter: casamayou | Owner: burcin
Type: defect | Status: new
Priority: major | Milestone: sage-4.7
Component: calculus | Keywords: integrate
Author: | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
-------------------------+--------------------------------------------------
In the following calculation, Sage4.6.2 returns the opposite of the right
result :
{{{
sage: var('a t')
(a, t)
sage: assume(a>0)
sage: assume(x>0)
sage: f = integrate(log(1+a/(x * t)^2), t, 1, oo)
sage: f
(sqrt(a)*x*log((x^2 + a)/x^2) - 2*a*arctan(sqrt(a)/x))/(sqrt(a)*x)
sage: f.subs(x=1, a=7).n()
-4.32025625668262
}}}
For information, Sage 4.6 gives the right result :
{{{
sage: var('a t')
(a, t)
sage: assume(a>0)
sage: assume(x>0)
sage: f = integrate(log(1+a/(x * t)^2), t, 1, oo)
sage: f
pi*sqrt(a)/x - (x*log((x2 + a)/x2) + 2*sqrt(a)*arctan(x/sqrt(a)))/x
sage: f.subs(x=1, a=7).n()
4.32025625668262
}}}
For information, Maple9 gives this :
{{{
> assume(a>0): assume(x>0):
> f := int(ln(1+a/(x * t)^2), t=1..infinity):
> lprint(f);
(2*ln(x)*x-2*a^(1/2)*arctan(x/a^(1/2))-ln(x^2+a)*x+a^(1/2)*Pi)/x
> evalf(subs(x=1, a=7, f));
bytes used=4000512, alloc=3341724, time=0.13
4.320256257
}}}
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11233>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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