Evaluate: `intxsinxcos^2x\ dx`

Explanation

`int_{a}^{b} f(x) d x=int_{a}^{b} f(a+b-x) d x`
`

Let I=int_{0}^{pi} x sin x cos ^{2} x d x ldots (1) `
`

Rightarrow int_{0}^{pi} x sin x cos ^{2} x d x=int_{0}^{pi}(pi-x) sin (pi-x) cos ^{2}(pi-x) d x `
`
Rightarrow As sin (pi-x)=sin x `
`
cos (pi-x)=-cos x `
`
=int_{0}^{pi} pi sin x cos ^{2} x d x-int_{0}^{pi} x sin x cos ^{2} x d x`
`
...