Don't worry! Integration by parts can be tricky at first, but once you get used to it you can get quite good at it. If you aren't sure at first which values to use for each "part," just take a good guess and see if you wind up with something simple enough to evaluate. If not, try again! You will get the hang of it.

In this case we want

.

The formula for integration by parts is

. Here's my suggestion: for

choose the most complicated portion of the integrand

*that you know how to integrate*. In our case,

is the most complicated factor, but it is integrated easily. So we would have

Once you make your substitutions, you will end up with

This integral,

, will require another application of integration by parts.

In general, here's some tips for choosing your

and

:

For integrals of the form

(and other trig functions), let

and

.

Similarly, for integrals of the form

, let

and

.

For the integrals

or

, let

or

, and let

. Use integration by parts twice, and you will actually end up with an equation that can be solved for the desired integral.

For integrals like

or

, let

be the entire integrand with

.