Intergral from p to infinity of F(p)dp = laplace of f(t)/t

I have to reverse the order of integration to show that those two are equivalent if F(p) = laplace of f(t)

Not sure how to do this, If i reverse the order of integration is it the integral from 0 to t?

Do i use the convolution theorem where g(u) = 1?

these are the ideas I have but not sure if it is right now not