Using Laplace transforms evaluate the following integrals. (a) \( \int_{0}^{\infty} t e^{-3 t} \cos 2 t d t \). (b) \( \int_{0}^{\infty} t e^{-2 t} \sin t d t \).

Question

Using Laplace transforms evaluate the following integrals.  

1. \( \int_{0}^{\infty} t e^{-3 t} \cos 2 t d t \). 
2.  \( \int_{0}^{\infty} t e^{-2 t} \sin t d t \).