- 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