can i have the complete solution for these problems ??
i don't know how to start solving !!
For the first one you will need to combine three different theorems
$\displaystyle \mathcal{L}\{ f'(t)\}=sF(s)-f(0)$
$\displaystyle \mathcal{L}\{ t^nf(t)\}=(-1)^n\frac{d^n}{ds^n}F(s)$
$\displaystyle \mathcal{L}\{ e^{at}f(t)\}=F(s-a) $
See if you can combine them to get the answer.
for 2 use the convolution theorem
$\displaystyle \mathcal{L}\{ \int_{0}^{t}f(t-\tau)g(\tau)d\tau\}=F(s)G(s)$