Evaluate: `intsin^3xcos^5x\ dx`

Explanation

`int sin ^{3} x cos ^{5} x d x `

`=int sin ^{3} x cos ^{2} x cos ^{3} x d x `

`=int sin ^{3} x(1-sin ^{2} x) cos ^{3} x d x `

`=int(sin ^{3} x-sin ^{5} x) cos ^{3} x d x `

`=int(sin ^{3} x-sin ^{5} x) cos ^{2} x cos x d x `

`=int(sin ^{3} x-sin ^{5} x)(1-sin ^{2} x) cos x d x `

`=int(sin ^{3} x-2 sin ^{5} x+sin ^{7} x) cos x d x `

`=int sin ^{3} x cos ^{x} d x-2 int sin ^{5} x cos x d x+int sin ^{7} x cos x d x `

...