Question

Evaluate ∫ x cos 3x dx.

Answer 1

This can be integrated using the method "integration by parts." The formula is

`\int{u\,dv}=uv-\int{v\,du}`

Here, it is convenient to assign

`u=x\\v=(1)/(3)sin((3x))`

Then you have

`\int{(xcos(3x))}\,dx=(1)/(3)xsin((3x))-\int{((1)/(3)sin((3x)))}\,dx\\\\=(1)/(3)xsin((3x))+(1)/(9)cos((3x))`