Trigonometric integral evaluation: $\int 4 \sin^4 x \cos^3 x \,dx$ Evaluate the following integral $$\int 4 \sin^4 x \cos^3 x \,dx$$
I can do simple integration problems, but problems like this seem to stump me, I created this problem so I could solve and compare it to another similar problem for my study guide, where should I start?

\begin{align}
4\int \sin^4{x}\cos^3{x}dx
&=4\int \sin^4{x}(1-\sin^2{x})\cos{x} \ dx\\
&=4\int \sin^4{x}-\sin^6{x} \ d(\sin{x})\\
&=\frac{4}{5}\sin^5{x}-\frac{4}{7}\sin^7{x}+c
\end{align}
