This is what the book says:
... but I'm not getting the same when I work through it, as follows:
Thus, let .
(by standard integrals)
(substituting for and )
I can't reconcile the given here with the as given above.
Now let .
This forces us to write the integrand in the form:
Substituting for and :
Again, this is different from how it appears in the source work.
The question is: who's got it wrong -- me or Murray R. Spiegel in his Mathematical Handbook of Formulas and Tables? He has been known to be wrong before.