Yes, that may work. But it wasn't what was most natural to me. I evaluated the integral on Wolfram Alpha for a couple of specific values and noticed that it was always of the form where that just screamed use a double integral to me.
Yes, that may work. But it wasn't what was most natural to me. I evaluated the integral on Wolfram Alpha for a couple of specific values and noticed that it was always of the form where that just screamed use a double integral to me.
The substitution is not something I came up with. My automatic approach would be to find the Cauchy principal value using contour integration and then drop the P.V. label because the integral is convergent.
But if you make that substitution you get
so
EDIT:
Last edited by Random Variable; June 14th 2011 at 06:43 PM.