first shifting

Problem 04
Evaluate   $\displaystyle \int_0^\infty \dfrac{e^{-t}\sin t}{t} ~ dt$.
 

Problem 03
Find the value of   $\displaystyle \int_0^\infty te^{-3t} \sin t ~ dt$
 

Problem 04
Find the Laplace transform of   $f(t) = e^t \sinh 2t$.