Compute the integral from 0 ---> infinity.
Hello e^17 is a constant in t so it can be pulled from the integrand and I am thinking you are looking for an integral table with the integand t^3e^-at from the expression I see in your request where a is (S+2). Where did this integral pop from is sometimes your first clue in finding it. I also typically look at the ...
An integral is evaluated by parts. The solution points toward the answer.