The Laplace transform of $e^{at}\sin\left ( bt \right )$ is
1. $\frac{b}{\left ( s-a \right )^{2}+b^{2}}$
2. $\frac{s-a}{\left ( s-a \right )^{2}+b^{2}}$
3. $\frac{s-a}{\left ( s-a \right )^{2}-b^{2}}$
4. $\frac{b}{\left ( s-a \right )^{2}-b^{2}}$