Why $\int{\log^2(2\sin(\pi x))}dx\neq\frac{\log^3(2\sin(\pi x))\sin(\pi x)}{3\pi \cos(\pi x)}$? Apparently I completely forgot the basics of calculus after 13 years of not studying it. Why won't:
$$\frac{d \log^2(2\sin(\pi x))}{dx} = \frac{\log^3(2\sin(\pi x))\sin(\pi x)}{3\pi \cos(\pi x)}$$

UPDATE:
Sorry everybody, I messed up the question big time. Yes, originally it's an integration question why won't:
$$\int{\log^2(2\sin(\pi x))}dx = \frac{\log^3(2\sin(\pi x))\sin(\pi x)}{3\pi \cos(\pi x)}$$

Using Chain rule:$$\frac{d }{dx}\log^2(2\sin(\pi x))=2\log(2\sin(\pi x))\times[2\times\pi\times\cos(\pi x)]\times\frac{1}{2\sin(\pi x)}$$
