Evaluate the following integral.

Question

Evaluate the following integral.

 

∫ x cos x dx

Answer 1

Use integration by parts:

 

 Let u = x         dv = cosxdx

      du = dx        v = ∫dv = sinx

 

∫xcosxdx = uv - ∫vdu

 

             = xsinx - ∫sinxdx  = xsinx + cosx + C