\int_0^a\int_0^b xy(x^2 - y^2)\dx\dy &= \int_0^a\int_0^b x^3y - xy^3\dx\dy\\ &= \int_0^a\frac{b^4}{4}y - \frac{b^2}{2}y^3\dy\\ \int_0^a\int_0^b xy\cos(x^2y + y)\dx\dy ...

I found Marsden and Weinstein's Calculus II/Calculus III books to be pretty decent, but it was years ago so I don't remember too well.

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