# 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.

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.

add a comment

2

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)
```

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.

Asked: **
2015-03-11 08:33:19 -0500
**

Seen: **256 times**

Last updated: **Mar 11 '15**

Is this a known bug with integral()

How to make typeset output in sage display properly?

integral() failing with "segmentation fault"

Integral not being computed correctly

Integrate() does not integrate

Variable type returned after integrating.

Error while integrate using algorithm='sympy' (bug)

How can I speed up symbolic function evaluation?

How can I Integrate the dirac_delta and heaviside functions in sage?

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.