What is the integral of 216sin(6x)\sqrt[3]{cos(6x)} ?

The integral of 216sin(6x)\sqrt[3]{cos(6x)} is -27cos^{4/3}(6x)+C

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integral of 216sin(6x)\sqrt[3]{cos(6x)}

- 27 cos^{\frac{4}{3}} (6 x) + C

Solution steps

Take the constant out:

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

Apply u-substitution

Take the constant out:

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

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{3}{4} v^{\frac{4}{3}}

= 216 \cdot \frac{1}{6} (- \frac{3}{4} v^{\frac{4}{3}})

Substitute back

= 216 \cdot \frac{1}{6} (- \frac{3}{4} cos^{\frac{4}{3}} (6 x))

Simplify

216 \cdot \frac{1}{6} (- \frac{3}{4} cos^{\frac{4}{3}} (6 x)) : - 27 cos^{\frac{4}{3}} (6 x)

= - 27 cos^{\frac{4}{3}} (6 x)

Add a constant to the solution

= - 27 cos^{\frac{4}{3}} (6 x) + C

\int \frac{π}{12} sin (\frac{π x}{6}) d x

\frac{d}{d x} (csc (x) (x + cot (x)))

2 sin (x^{2})

f (x) = 2 x^{3} + 3 x^{2} - 12 x + 7

x \to \infty lim (- 10 e^{- 2 x})

What is the integral of 216sin(6x)\sqrt[3]{cos(6x)} ?
The integral of 216sin(6x)\sqrt[3]{cos(6x)} is -27cos^{4/3}(6x)+C