Inverse laplace transform of $\frac{s}{s+a}$

Question

There is a missing entry in my table of Laplace transforms. I want to make a transform of the general form of the fraction

$$\frac{s}{s+a}$$

Using the definition:

$$\mathscr{L}^{-1}\{F(s)\}=\frac{1}{2\pi i}\int_{\gamma-iT}^{\gamma+iT}e^{st}F(s)ds$$

But this becomes messy with integration by parts and even wolfram doesn't solve it.

$$\frac{1}{2\pi i}\int_{\gamma-iT}^{\gamma+iT}e^{st}\frac{s}{s+a}ds$$

The answer should be $f(t)=\delta(t)-9e^{-9t}$

Any ideas how to get that from the tables?

Thanks