What is the integral of (1+cos(2θ)) ?

The integral of (1+cos(2θ)) is θ+1/2 sin(2θ)+C

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integral of (1+cos(2θ))

\int (1 + cos (2 θ)) d θ

θ + \frac{1}{2} sin (2 θ) + C

Solution steps

\int 1 + cos (2 θ) d θ

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 θ + \int cos (2 θ) d θ

\int 1 d θ = θ

\int cos (2 θ) d θ = \frac{1}{2} sin (2 θ)

= θ + \frac{1}{2} sin (2 θ)

Add a constant to the solution

= θ + \frac{1}{2} sin (2 θ) + C

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What is the integral of (1+cos(2θ)) ?
The integral of (1+cos(2θ)) is θ+1/2 sin(2θ)+C