# Integration by Parts Problems where You Go around in Circles

Sometimes if you use integration by parts twice, you get back to where you started from — which, unlike getting lost, is not a waste of time.

First, use the *LIATE* mnemonic device to pick your *u**:*

To pick your *u*, go down this list in order; the first type of function on this list that appears in the integrand is the *u.*

Now fast forward to the formula step:

Now, substitute the right side of the above equation for the

from the original solution:

You can now solve this equation for the integral

Use *I* in place of that integral to make this messy equation easier on the eyes:

Add *I* to both sides:

Multiply both sides by 1/2: