# Math Help - Stuck on simple integral

1. ## Stuck on simple integral

Hey all, stuck on a simple integrand..

$\int_0^\frac{\pi}{3} \! xcos(2x) \, \mathrm{d}x.$

I get..

$u = cos(2x) \; dv = xdx \; du = -2sin(2x) \; v = \frac{x^2}{x}$

$\int xcos(2x) dx = uv - \int vdu \Rightarrow \frac{x^2}{x}cos(2x) - \int -x^2sin(2x)$

Problem is the new integral isn't any easier to solve..

2. You nearly always choose the polynomial function to be $\displaystyle u$, because differentiating reduces its power, and eventually becomes a constant...

3. Do you know "ILATE" rule? According to that u should be x and dv should be cos(2x). Now try.