Question

How to integrate this

Answer 1

To integrate, let's first clean out the inside, and simplify:

`16\int {(sin x)^4} \ dx`

We can now safely substitute the value of u:

`u = sin x`

`du = cos (x) dx`

Now, we can write that:

`16\int{u^4} \ du`

This is much easier to integrate:

`16\int{u^4} \ du = 16[(1)/(5)u^5] + C`

Simplify:

`(16)/(5)u^5 + C`

Replace u (final answer):

`(16)/(5)sin^5x +C`

Hope I could help with your integration.