How to integrate this

Question

asked Sep 18, 2019 41.6k views

1 Answer

Sergii Pechenizkyi · Answer 1 · 2019-09-22T05:28:44+0000

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.