I've done a pretty similar one, but for this one I don't get what I should get. I post the integral and my steps : .
Let , .
. Let . . But as and , we have that , backsub I get . Putting the limits I finally get that is worth since . But the answer should be according to Mathematica...
I didn't see my error even when typing all this in Latex. Note that for simplicity I didn't take in count the limits of the integral, so it's not mathematically correct to say that is worth all the steps I did before to get to the last value (from which it should be equal to, but it seems it isn't).