Re: integration problem

mira <mirek.hyza@xxxxxxxxx> wrote:
Hello,

Integrate[x^(2 n + 1)/(1 + x^2), {x,0,1}], n...integer

It can be given in closed form in terms of the digamma function:

( digamma((n + 2)/2) - digamma((n + 1)/2) )/4

For information about the digamma function, see
<http://functions.wolfram.com/GammaBetaErf/PolyGamma/>, for example.

In case it would be of interest:
For large n, the integral is approximately 1/(4n + 2).

David
.