Let and be constants with at least one of them nonzero and define

Using integration by parts, establish the following formulas for constants ,

Using these formulas prove the following integration formulas,

To establish the formula we use integration by parts letting

Then we can evaluate using the formula for integration by parts,

To establish the second formula, , we use integration by parts again. Let

Then we have

This establishes the two requested equations, now we prove the two integral identities.

* Proof. * Solving for in the second equation above we have

Plugging this into the first equation we have

Next, for the second integral equation we are asked to prove, we use the formula we obtained for above,

Then, we use the expression we obtained for into this,

This implies,