Thread: improper integral #6 (three parameters)

1. improper integral #6 (three parameters)

They can be viewed as either Laplace transforms or Mellin transforms.

$\int_{0}^{\infty} e^{-ax} \cos (bx) x^{s-1} \ dx \ \ \ a,s>0$

and $\int_{0}^{\infty} e^{-ax} \sin (bx) x^{s-1} \ dx \ \ \ a,s>0$