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

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

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integral of 2cos^2(x)-1

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

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

Solution steps

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

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

\int 1 d x = x

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

Simplify

= \frac{1}{2} sin (2 x)

Add a constant to the solution

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

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