Is there any reference showing how to do definite integrals involving the complete elliptic integral of the first kind K(k)? Something like
 $\int_0^1 K(k) dk $
 $\int_0^1 k^nK(k) dk$
 $\int_0^1 \frac{K(k)}{1+k} dk $
etc...Thanks a lot.
Is there any reference showing how to do definite integrals involving the complete elliptic integral of the first kind K(k)? Something like
etc...Thanks a lot. 

