No. 390.

This is what the book says:

... but I'm not getting the same when I work through it, as follows:

Weierstrass substitution:

delivers:

Let .

Then:

Thus, let .

Then:

(by standard integrals)

(substituting for and )

I can't reconcile the given here with the as given above.

Now let .

Then:

Thus, let:

or:

This forces us to write the integrand in the form:

(standard integral)

Substituting for and :

after simplifying

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.