What is the integral of cos^2(2x+4) ?

The integral of cos^2(2x+4) is x-1/8 (2(2x+4)-sin(2(2x+4)))+C

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integral of cos^2(2x+4)

\int cos^{2} (2 x + 4) d x

x - \frac{1}{8} (2 (2 x + 4) - sin (2 (2 x + 4))) + C

Solution steps

\int cos^{2} (2 x + 4) d x

Rewrite using trig identities

= \int 1 - sin^{2} (2 x + 4) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x - \int sin^{2} (2 x + 4) d x

\int 1 d x = x

\int sin^{2} (2 x + 4) d x = \frac{1}{8} (2 (2 x + 4) - sin (2 (2 x + 4)))

= x - \frac{1}{8} (2 (2 x + 4) - sin (2 (2 x + 4)))

Add a constant to the solution

= x - \frac{1}{8} (2 (2 x + 4) - sin (2 (2 x + 4))) + C

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What is the integral of cos^2(2x+4) ?
The integral of cos^2(2x+4) is x-1/8 (2(2x+4)-sin(2(2x+4)))+C