# 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

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.

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)
```

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Asked: ** 2015-03-11 14:33:19 +0200 **

Seen: **1,266 times**

Last updated: **Mar 11 '15**

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