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

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

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integral of cos^2(kx)

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

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

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

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

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

Add a constant to the solution

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

\int_{2}^{4} \frac{x}{x ^{2} + 6 x + 13} d x

n = 0 \sum \infty \frac{1}{n ^{2}}

\frac{\partial}{\partial x} (e^{6 x + 9 y})

y = \frac{1}{2} x, y = 1, y = \frac{1}{25} x^{2}

n = 5 \sum \infty sin (\frac{1}{n ^{2}})

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