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: