Using integration by parts, prove the following formula:
Use this solution to evaluate
Proof. To apply integration by parts, first define
Where the formula for follows since we can evaluate
by making the substitution
which implies
; therefore, we have
Then, using integration by parts, we have the following:
Now, applying the formula to , we first note that since
this is the case of the above formula with
. Therefore,
Then, for we have