this example is a integration by parts problem.

∫udv= uv- ∫vdu. ( use the integration by parts formula)

2∫xcos 5x

u = x. du = 1dx. dv =cos(5x). v = ∫cos(5x)dx

sin (5x) 5 dx = 1/5 sin (5x)

1/5 x sin(5x) – ∫ 1/5 sin(5x) 1 dx

1/5x sin(5x) – 1/5 ∫sin(5x) dx

1/5 x sin(5x)- 1/5.(1/5) cos (5x) this is what u get by integrating ∫sin(5x)

2 ( 1/5 x sin(5x) +1/25 cos (5x) +C

2/5 x sin(5x) +2/25 cos (5x) +C. final answer.