Answer
$$\eqalign{
& {\text{Split off }}\cos x,{\text{ rewrite the resulting even power of }} \cr
& \cos x{\text{ in terms of }}\sin x,{\text{ and then use }}u = \sin x \cr} $$
Work Step by Step
$$\eqalign{
& {\text{Let the integrand:}} \cr
& {\text{si}}{{\text{n}}^m}x{\cos ^n}x,\,\,\,\,\,\,{\text{With: }}\,\,\,\,m{\text{ even }}\,\,\,\,\,\,{\text{and }}\,\,\,\,\,n{\text{ odd}} \cr
& {\text{The strategy of integration would be}} \cr
& {\text{Split off }}\cos x,{\text{ rewrite the resulting even power of }} \cr
& \cos x{\text{ in terms of }}\sin x,{\text{ and then use }}u = \sin x \cr
& Example{\text{:}} \cr
& \int {{{\sin }^m}x\cos \overbrace {^{2k + 1}}^{{\text{Odd}}}xdx} = \int {{{\sin }^m}x\overbrace {{{\left( {{{\cos }^2}x} \right)}^k}}^{{\text{Convert to sines}}}\overbrace {\cos xdx}^{{\text{Save for }}du}} \cr} $$
