Integrate $\sqrt{(1-\cos(x))^3}$ I need help solving the following integration problem:
$$\int \sqrt{(1-\cos(x))^3} dx$$
I know I am supposed to use a trig identity so that I can do a u-sub, but don't know which one or how.

Hint:
Since $\cos(2x) = 1 - 2 \sin^2(x)$, $1-\cos x = 2 \sin^2(\frac{x}{2})$:
$$\int 2 \sqrt{2} \ \bigg(\sin^2\left(\frac{x}{2}\right)\bigg)^{3/2}  dx$$
$$= 2\sqrt{2} \int \left| \ \sin^3\left(\frac{x}{2}\right) \right| dx$$
Now from $\sin(3x) = 3 \sin x - 4 \sin^3 x$, $4 \sin^3(x) = 3 \sin(x) - \sin(3x)$, so you can use the identity $\sin^3(x) = \frac{3}{4}\sin(x) - \frac{1}{4}\sin(3x)$.
