Integrate.

Answer

We need to use the factoring trick on this one. If we break up *x*^{3} so that one *x* goes with (1 + *x*^{2})^{-3}, we'll have a nice candidate for *v*'.

Take

*u* = *x*^{2}

*v'* = *x*(1 + *x*^{2})^{-3}

Then

Putting this into the formula, we get

The new integral can be evaluated by substitution, taking *u* = (1 + *x*^{2}), and we get