Question

Evaluate : `int  x cosx dx`

Answer 1

Let I = `int  xcosx dx`

Integrating by parts

∴ I = x `int cosx dx - int [d/dx (x) int cos x dx]dx`
= `xsinx - int 1(sin x) dx + c`

= `xsinx - ( - cos x) + c`

= `xsinx + cos x + c`