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: