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,