Primitive of Exponential of a x by Sine of b x/Proof 2

Theorem

 * $\displaystyle \int e^{a x} \sin b x \ \mathrm d x = \frac {e^{a x} \left({a \sin b x - b \cos bx}\right)} {a^2 + b^2} + C$

Proof
The result follows from equating imaginary parts.