Question

Integrate the following by parts |xcos x dx​

Answer 1

`\displaystyle \int x \cos x ~dx\\\\=x\displaystyle \int \cos x ~dx- \displaystyle \int \left((d)/(dx) x \displaystyle \int \cos x ~dx \right) dx\\\\=x\sin x - \displaystyle \int\left( \sin x \right) dx\\ \\=x \sin x - (-\cos x) +C\\\\=x \sin x + \cos x +C`