Consider using these strategies, when integrating rational functions:
(S1) Use long-division, if the expression is improper.
(S2) Use partial fractions, if the denominator can be factorised.
(S3) Complete the square, if the denominator cannot be factorised. This usually leads to a recognisable integral.
(S4) Use integrals of recognisable forms.
See example 1, example 2, example 3.
Try this: Mathematics 9233 Nov '05/Paper 1/Q14 Either