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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. $\frac{b}{\left ( s-a \right )^{2}-b^{2}}$
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