Integrals — Class 12 Maths Solution

Let $I = \int {x\sin xdx} = x\int {\sin xdx} - \int {\left[ {\cfrac{d}{{dx}}\left( x \right)\int {\sin xdx} } \right]} dx$

$= x\left( { - \cos x} \right) - \int {1 \cdot \left( { - \cos x} \right)dx} = - x\cos x + \int {\cos xdx}$

$= - x\cos x + \sin x + C$