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

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

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integral of cos^2(X)

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

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

Solution steps

\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

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