What is the integral of sin(18x)\sqrt[3]{cos(18x)} ?

The integral of sin(18x)\sqrt[3]{cos(18x)} is -1/24 cos^{4/3}(18x)+C

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integral of sin(18x)\sqrt[3]{cos(18x)}

- \frac{1}{24} cos^{\frac{4}{3}} (18 x) + C

Solution steps

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}}

= \frac{1}{18} (- \frac{3}{4} v^{\frac{4}{3}})

Substitute back

= \frac{1}{18} (- \frac{3}{4} cos^{\frac{4}{3}} (18 x))

Simplify

\frac{1}{18} (- \frac{3}{4} cos^{\frac{4}{3}} (18 x)) : - \frac{1}{24} cos^{\frac{4}{3}} (18 x)

= - \frac{1}{24} cos^{\frac{4}{3}} (18 x)

Add a constant to the solution

= - \frac{1}{24} cos^{\frac{4}{3}} (18 x) + C

\int cos (2 v) d v

\frac{d}{d x} (x, x)

\frac{d}{d x} (\frac{b}{a} a^{2} - x^{2})

\frac{\partial}{\partial T} (\frac{x}{T})

5 \cdot 3^{x}

What is the integral of sin(18x)\sqrt[3]{cos(18x)} ?
The integral of sin(18x)\sqrt[3]{cos(18x)} is -1/24 cos^{4/3}(18x)+C