The exact method used to integrate the partial fractions of a
given fraction cannot be predicted without knowing the exact form
of the partial fraction. I list below some examples: If the partial
fractions are of the form 1/(ax+b) where a and b are constants and
x is the dummy variable, the integral will be (1/a) ln(|(ax+b)|)+C,
where C is the integration constant. You may solve denominators of
second degree by using method of completion of squares.