To integrate, let's first clean out the inside, and simplify:
[tex]16\int {(sin x)^4} \ dx[/tex]
We can now safely substitute the value of u:
[tex]u = sin x[/tex]
[tex]du = cos (x) dx[/tex]
Now, we can write that:
[tex]16\int{u^4} \ du[/tex]
This is much easier to integrate:
[tex]16\int{u^4} \ du = 16[\frac{1}{5}u^5] + C[/tex]
Simplify:
[tex]\frac{16}{5}u^5 + C[/tex]
Replace u (final answer):
[tex]\frac{16}{5}sin^5x +C[/tex]
Hope I could help with your integration.
