Question

Can anyone think of a single integration problem that requires a combination of partial fraction decomposition, substitution, and integration by parts to be able to solve it?

Answer 1

think of one? no, but im sure they are lurking out there someplace :)

Answer 2

lets try this one:
integral(sec^3(x) + sin^2(x))dx
you have substitution: u=2x; & sec^3 - int by parts...
add some fraction & you'll have what you need