Primitive of Exponential of a x by Power of Sine of b x/Lemma 2

Lemma for Primitive of $e^{a x} \sin^n b x \cos b x$

 * $\dfrac {a^2 + n b^2} a e^{a x} \sin^n b x - \dfrac {n b} a e^{a x} \sin^{n - 1} b x \left({a \cos b x + b \sin b x}\right) = e^{a x} \sin^{n - 1} b x \left({a \sin b x - n b \cos b x}\right)$