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

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

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integral of cos^2(wx)

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

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

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

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

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

Add a constant to the solution

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

f (x) = 3 sec (x), at x = \frac{π}{6}

\int \frac{1}{7 x - 1} d x

x \to 0 lim (\frac{sin ( \frac{x}{4} )}{x})

\int cos^{3} (x) tan^{2} (x) d x

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