What is the integral of cos^2(x/2) ?

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

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integral of cos^2(x/2)

integral

cos^{2} (\frac{x}{2})

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

Solution steps

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

Rewrite using trig identities

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

\int 1 d x = x

\int cos (x) d x = sin (x)

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

Add a constant to the solution

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

\frac{1}{( x + a ) ^{2}}

\frac{1}{( 2 n - 1 ) ^{2}}

\frac{2 x}{x + 2}

\frac{x ^{2}}{( x ^{2} + x + 1 ) ^{2}}

(sin (x) + cos^{2} (x))^{3}

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