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

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

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integral of (cos(x))^2

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

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

Solution steps

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

Simplify

= \int cos^{2} (x) d x

Rewrite using trig identities

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 + cos (2 x) 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

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

\int 1 d x = x

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

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

Add a constant to the solution

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

\int_{0}^{1} x (x - x) d x

\frac{d}{d x} (ln (x - 2))

\int_{0}^{π} (5 e^{x} + 5 sin (x)) d x

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

\int \frac{- x + 2}{x + 1} d x

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