# 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: **392 times**

Last updated: **Mar 11 '15**

Integration and differentiation symbols

Strange behviour when trying to integrate gaussian function. bug?

Integrating with constant integrand

integral() failing with "segmentation fault"

symbolic and numeric double integration method

What is the problem with that integral ?

Two ways of integrating x↦xⁿsin(x) give contradictory results. Bug?

Mathcad 14 Help required [closed]

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.