How do you do integration by parts?

When you see a complicated product, split it into the form u.v', where u and v' are algebraic expressions such as x^2. You can then use the formula: uv'=uv-integral(vu') which you would take between any limits.

The important thing to do is to choose u and v' well, as you need to differentiate u and integrate v'. Make sure this is possible, and that one of the two operations, usually differentating u, will make the integral of vu' solvable without integration by parts, or with only one more application of it.