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

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Answer 1 · 2016-07-18T11:37:48

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

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

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

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