# 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 -0600
**

Seen: **369 times**

Last updated: **Mar 11 '15**

Integral not being computed correctly

Maxima crashes on relatively simple integral

ValueError: Computation failed since Maxima requested additional constraints

How can I speed up symbolic function evaluation?

How to do numerical integral where the answer still have variables in it?

Plotting an integral with a variable as a limit

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.