Question

∫ x*sinx dx

Answer 1

We use integration by parts method.

Let u = x, which implies du/dx = 1

and let dv/dx = sin(x). Integrating this to get v gives v = –cos(x).

$∫ x sin(x) dx = ∫ u(dv/dx) dx = uv – ∫ v(du/dx) dx = –x cos(x) – ∫ –cos(x)*1 dx = –x cos(x) – ∫ –cos(x) dx = –x cos(x) + ∫ cos(x) dx = –x cos(x) + sin(x) + c.$