What is the integral of 2cos^2(θ)-1/2 ?

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

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integral of 2cos^2(θ)-1/2

\int 2 cos^{2} (θ) - \frac{1}{2} d θ

\frac{1}{2} θ + \frac{1}{2} sin (2 θ) + C

Solution steps

\int 2 cos^{2} (θ) - \frac{1}{2} 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 2 cos^{2} (θ) d θ - \int \frac{1}{2} d θ

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

\int \frac{1}{2} d θ = \frac{1}{2} θ

= θ + \frac{1}{2} sin (2 θ) - \frac{1}{2} θ

Simplify

θ + \frac{1}{2} sin (2 θ) - \frac{1}{2} θ : \frac{1}{2} θ + \frac{1}{2} sin (2 θ)

= \frac{1}{2} θ + \frac{1}{2} sin (2 θ)

Add a constant to the solution

= \frac{1}{2} θ + \frac{1}{2} sin (2 θ) + C

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