Question

Evaluate:

`int x^2 cos x  dx`

Answer 1

Let I = `int x^2 cos x  dx`

On applying integration by parts

I = `x^2 int cos x  dx - int{d/dx (x^2) int cosx.dx}dx`

I = `x^2 sinx - int 2x sinx  dx`

Again on applying integration by parts

= x² sin x – 2[– x cos x – ∫ – cos x dx]

= x² sin x – 2[– x cos x + sin x + c]

= x² sin x + 2x cos x – 2 sin x + c

= (x² – 2) sin x + 2x cos x + c