Solve this indefinite integral:

I am offering 50 points for this question.

2 ( x sin x + cos x) + c  where c is the constant of integration

Step-by-step explanation:

∫ 2x cos x dx

2 ∫ x cos x dx

Use integration by parts

u = x     dv = cos x

du = 1     v = sin x

∫ u v =  u v - ∫v du

∫ x cos x dx =  x sinx - ∫ sin x *1

                     = x sin x -  (- cos x)

                      = x sin x + cos x

2 ∫ x cos x dx = 2 ( x sin x + cos x) + c where c is the constant of integration