What is the integral of cos^2(1/3)x ?

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

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integral of cos^2(1/3)x

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

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

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: \frac{x ^{2}}{2}

= cos^{2} (\frac{1}{3}) \frac{x ^{2}}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{cos ^{2} ( \frac{1}{3} ) x ^{2}}{2}

Add a constant to the solution

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

\frac{\partial}{\partial x} (x + y - 1)

\int (t^{2} + 1)^{2} d t

\int_{- \infty}^{9} r e^{\frac{r}{3}} d r

\int \frac{4}{x 1 + 2 x} d x

\frac{\partial}{\partial x} (x \cdot e^{- \frac{y}{x}})

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