improper integral error?
Is there an alternative way to calculate this improper integral?
integral(log(x)/(x^2 - 1),x,0,infinity)
the integral is convergent to pi^2/4 but Sage says divergent.
Is there an alternative way to calculate this improper integral?
integral(log(x)/(x^2 - 1),x,0,infinity)
the integral is convergent to pi^2/4 but Sage says divergent.
Always try the other available "algorithms":
sage: integral(log(x)/(x^2 - 1),x,0,infinity, algorithm='mathematica_free')
-1/2*log(x + 1)*log(x) - 1/2*polylog(2, -x) - 1/2*polylog(2, -x + 1)
With the algorithm set to mathematica_free
, Sage is returning the antiderivative even though you are asking for the improper integral. You can get the improper integral by doing the following:
f=integral(log(x)/(x^2 - 1),x,algorithm='mathematica_free')
limit(f,x=oo)-limit(f,x=0)
This returns pi^2/4.
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Asked: 2015-03-11 14:33:19 +0100
Seen: 1,354 times
Last updated: Mar 11 '15
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