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

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

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integral of cos^2(r)

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

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

Solution steps

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

Rewrite using trig identities

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

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 r) d r

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 r + \int cos (2 r) d r)

\int 1 d r = r

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

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

Add a constant to the solution

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

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