Does the denominator factorise? If not, then partial fractions is not appropriate.

First look for simple substitutions. If you make the substitution , then you require its derivative to be a factor. We can easily get that...

So the first term can be easily integrated using that substitution. The second requires completing the square on the denominator, then it should either look familiar (as the derivative of an inverse trigonometric or hyperbolic function) or will require a trigonometric or hyperbolic substitution.