Question #43621

1 Answer
Jan 15, 2018

intsin(4x)cos^2(4x)dx = - cos^3(4x)/12 + C

Explanation:

By evaluating, I'm assuming you mean integration.

To begin, use substitution:
u = cos(4x), du = -4sin(4x)dx or (du)/(-4sin(4x)) = dx

Then proceed and we will get that the integral is now:
-1/4intu^2du
Notice that when we used substitution, we found that (du)/(-4sin(4x)) = dx and when we substituted dx with (du)/(-4sin(4x)), we can cancel out sin(4x). This leaves us with the new integral above.

Then integrating that is a simple matter, so: (-1/4)u^(2+1)/(2+1) + C which is basically -u^3/12. Then we reverse our substitution, and we would get our answer: -cos^3(4x)/12 + C.