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)?

Helpful Tutorials on integration by inspection

Step 2(b): If not of the above type, try integration by parts or substitution.

STEP 3: Is it a fraction?