I am of often asked, “What method do we use in order to work out an integral?”
There is no exact set of rules but a systematic approach following these guidelines should help for integrals at this level.
Try step 1 first and if it is not true go on to step 2, then 3 until a method is found.
STEP 1: Is it a standard Integral?
STEP 2(a): Is it a product of the form f[g(x)]g'(x)?
Step 2(b): If not of the above type, try integration by parts or substitution.
STEP 3: Is it a fraction?