Primitive of Power of x by Cosine of a x/Corollary

Theorem

 * $\displaystyle \int x^m \cos a x \rd x = \sum_{k \mathop = 1}^{m + 1} \paren {m^{\underline {k - 1} } \frac {x^{m + 1 - k} } {a^k} \map {\sin} {x + \dfrac {\pi} 2 \paren {k - 1} } }$

where $m^{\underline {k - 1} }$ denotes the $k - 1$th falling factorial of $m$.