Laplace Transform of Exponential times Sine

Theorem

 * $\map {\laptrans {e^{b t} \sin a t} } s = \dfrac a {\paren {s - b}^2 + a^2}$

where:
 * $a$ and $b$ are real numbers
 * $s$ is a complex number with $\map \Re s > a + b$
 * $\laptrans f$ denotes the Laplace transform of $f$ evaluated at $s$.