Laplace Transform

Help me solve this problems.Thanks. :)

Laplace of e^5t+1(t sin (t))

Can you help with the laplace transform of derivative of sin (at)

This is for Inverse Laplace Transform.

What will the Region of Convergence (Pole-zero plot) look like if the pole is equal to zero? The zeroes or the numerator has values but the poles or the denominator is just s.