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.

$$\int \sqrt{\left(1-\cos \left(x\right)\right)^3} = 4\sqrt{2}\int \:\frac{y^3}{\left(1+y^2\right)^{\frac{5}{2}}}dy=2\sqrt{2}\int \:\frac{1}{z^{\frac{3}{2}}}-\frac{1}{z^{\frac{5}{2}}}dz$$
You will get this result by applying these substitutions in sequence
$$y=\tan\left(\frac{x}{2}\right)\qquad\qquad z= 1+y^2$$
$$\int \sqrt{\left(1-\cos \left(x\right)\right)^3}=\color{red}{4\sqrt{2}\left(\frac{1}{3\sec ^3\left(\frac{x}{2}\right)}-\frac{1}{\sec \left(\frac{x}{2}\right)}\right)+C}$$
