Question

How do you find the integral of `cos^(2)2xdx`?

Answer 1

`int cos^2(2x) dx = 1/2int cos(4x)dx + 1/2x + C`

Explanation:

Using the fact

`cos(a+b)=cos(a) cos(b)-sin( a) sin(b)` we know that
`cos(2a) = 2cos^2(a)-1` then
`cos^2(a)=(cos(2a)+1)/2`

so

`cos^2(2x) =(cos(4x)+1)/2` and finally

`int cos^2(2x) dx = 1/2int cos(4x)dx + 1/2x + C`