Integral of Product of Exponential with Sine or Cosine

Theorem

Primitive of $e^{a x} \sin b x$

$\ds \int e^{a x} \sin b x \rd x = \frac {e^{a x} \paren {a \sin b x - b \cos b x} } {a^2 + b^2} + C$

Primitive of $e^{a x} \cos b x$

$\ds \int e^{a x} \cos b x \rd x = \frac {e^{a x} \paren {a \cos b x + b \sin b x} } {a^2 + b^2} + C$