Integrate xsin(x) with respect to x

For this use integration by parts, letting the integral = T. Let u = x and dv/dx = sin(x). Differentiating u with respect to x gives du/dx = 1. Integrating dv/dx with respect to x gives v = - cos(x). Now, using the integration by parts formula, we get T = - xcos(x) - integral of (-cos(x)). Then, integrating this gives T = sin(x) - xcos(x) + c (where c is a constant).