What is the integral of cos^7(1/3)x ?

The integral of cos^7(1/3)x is (cos^7(1/3)x^2)/2+C

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integral of cos^7(1/3)x

\int cos^{7} (\frac{1}{3}) x d x

\frac{cos ^{7} ( \frac{1}{3} ) x ^{2}}{2} + C

Solution steps

\int cos^{7} (\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^{7} (\frac{1}{3}) \cdot \int x d x

Apply the Power Rule

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

= cos^{7} (\frac{1}{3}) \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{cos ^{7} ( \frac{1}{3} ) x ^{2}}{2}

Add a constant to the solution

= \frac{cos ^{7} ( \frac{1}{3} ) x ^{2}}{2} + C

\int 12 x^{2} - 6 x d x

\frac{\partial}{\partial x} (2 x y - y e^{\frac{y}{z}})

\int 1 + \frac{1}{x ^{\frac{2}{3}}} d x

x \to 1 lim (5 x^{2} + 1)

y = x^{2} + 4 x + 9, at x = 8

What is the integral of cos^7(1/3)x ?
The integral of cos^7(1/3)x is (cos^7(1/3)x^2)/2+C