Question

Evaluate the integral: ∫x² cos x dx

Answer 1

It is given that

∫x² cos x dx

We can write it as

By integrating w.r.t x

= x² sin x – ∫2x sin x dx

So we get

= x² sin x – 2 [∫ x sin x dx]

Now apply by the part method

= x² sin x – 2 ∫ x sin x dx

Again by integration

We get

= x² sin x – 2 [x (- cos x) – ∫ 1. (- cos x) dx]

By integrating w.r.t x

= x² sin x – 2(- x cos x + sin x) + c

On further simplification

= x² sin x + 2x cos x – 2 sin x + c