- Let
Use integration by parts to prove
- Using part (a), prove that
- Proof. First, to apply integration by parts define
Then, we apply integration by parts to compute,
Thus, adding
to both sides we have
- Proof. First from the definition of
, letting
we have
Then, using the formula in the solution of part (a) we have
Then, again using the formula in the solution of part (a) we have
Now, to evaluate this integral we use the method of substitution, letting
implies
. So,
So, plugging this solution back into our formula for
we have
Then, using this solution in the formula for
we have