Use Integration by parts to find ∫ xsin3x dx

∫ xsin3x dx takes the form of any integral ∫ (u)(dv/dx) dx.
∫ (u)(dv/dx) dx = uv - ∫ (v)(du/dx) dx
Taking u=x and dv/dx= sin3x. The equation can be re-written in the form uv - ∫ (v)(du/dx) dx.
Therefore, ∫ xsin3x dx = (x)(-1/3cos3x) - ∫ (-1/3cos3x)(1) dx .
= -x/3cos3x + 1/3 ∫ cos3x dx
= -x/3cos3x + 1/9 sin3x + c