Question

How do you integrate `int xsin2x` by integration by parts method?

Answer 1

`int xsin2xdx = -1/2xcos2x +1/4sin2x`

Explanation:

As:

`d(cos2x) =-2sin2x dx`

we can integrate by parts in this way:

`int xsin2xdx = -1/2 int x d(cos2x) = -1/2 xcos2x +1/2 int cos2x dx= -1/2xcos2x +1/4sin2x`