I have to find Laplace transform of:

$\displaystyle \frac{1}{4}t^7e^\frac{-1t}{2}$

Here is what I have:

$\displaystyle \frac{1}{4}\frac{7!}{s^8}\frac{1}{s+\frac{1}{2}}$

which simplifies to:

$\displaystyle \frac{1260}{s^8(s+\frac{1}{2})}$

Is this ok??

Also, I have to find inverse Laplace of:

$\displaystyle \frac{-8}{(s-7)^5}$

Do I need to use partial fractions on this, or is there a simpler way?

Thanks