If the integrand is
then the easiest way to compute this is to expand the product completely, then integrate the resulting polynomial.
If instead it's
you can split the integrand into partial fractions
On the right side, we have
so that
Then
In both denominators, we can complete the square to write
Then substitute
We have
Since
and
all the remaining integrals are trivial; we end up with
Reverse the substitution: