A rational function can be rewritten using what is known as partial fraction decomposition. This procedure often allows integration to be performed on each term separately by inspection. For each factor of the form , introduce terms

For each factor of the form , introduce terms

Then write

and solve for the s and s.

Partial fraction decomposition is implemented in the Wolfram Language as Apart.

More things to try:

Weisstein, Eric W. "Partial Fraction Decomposition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PartialFractionDecomposition.html