i have to solve by using Laplace transforms and then inverting it using contour integration (which i'm incredibly vague on)

we were given the rule that if then , and also that the Laplace transform of an integral is

i found the Laplace transform of is and of is

do i have to Laplace transform the integral on the left as well? or do I multiply both Laplace transforms together and then integrate by contour integration?

i'm a little confused as to what to do next!