What is the integral of cos^2(x/3) ?

The integral of cos^2(x/3) is 1/2 (x+3/2 sin((2x)/3))+C

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integral of cos^2(x/3)

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

\frac{1}{2} (x + \frac{3}{2} sin (\frac{2 x}{3})) + C

Solution steps

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

Rewrite using trig identities

= \int \frac{1}{2} (1 + cos (\frac{2 x}{3})) 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 (\frac{2 x}{3}) 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 (\frac{2 x}{3}) d x)

\int 1 d x = x

\int cos (\frac{2 x}{3}) d x = \frac{3}{2} sin (\frac{2 x}{3})

= \frac{1}{2} (x + \frac{3}{2} sin (\frac{2 x}{3}))

Add a constant to the solution

= \frac{1}{2} (x + \frac{3}{2} sin (\frac{2 x}{3})) + C

\int_{- \infty}^{- 1} e^{- 38 t} d t

n = 1 \sum \infty \frac{5}{n ^{2} + 16}

s^{2} + 6 s + 7

x \to \frac{π}{2} lim (x)

y = \frac{7 ln ( x )}{3 x + 4}

What is the integral of cos^2(x/3) ?
The integral of cos^2(x/3) is 1/2 (x+3/2 sin((2x)/3))+C