I have to compute$$\int\_0^\infty \dfrac{e^{-tx}\cdot \sin(x)}{x}dx$$

This is following a helping problem $$\int\_0^\infty e^{-tx}\cdot \sin(x)dx$$ which using IPB two times turned out to be $$\dfrac{1}{1+t^2}$$

I think there must be a substitution to get to the first problem, but I just cannot see it. Any hint appreciated.