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

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

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integral of cos^2(s)

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

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

Solution steps

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

Rewrite using trig identities

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

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 s) d s

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

\int 1 d s = s

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

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

Add a constant to the solution

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

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