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

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

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integral of cos^2(mx)

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

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

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

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

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

Add a constant to the solution

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

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