What is the integral of sin(4x)\sqrt[3]{cos(4x)} ?

The integral of sin(4x)\sqrt[3]{cos(4x)} is -3/16 cos^{4/3}(4x)+C

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integral of sin(4x)\sqrt[3]{cos(4x)}

- \frac{3}{16} cos^{\frac{4}{3}} (4 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}{4} (- \frac{3}{4} v^{\frac{4}{3}})

Substitute back

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

Simplify

\frac{1}{4} (- \frac{3}{4} cos^{\frac{4}{3}} (4 x)) : - \frac{3}{16} cos^{\frac{4}{3}} (4 x)

= - \frac{3}{16} cos^{\frac{4}{3}} (4 x)

Add a constant to the solution

= - \frac{3}{16} cos^{\frac{4}{3}} (4 x) + C

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What is the integral of sin(4x)\sqrt[3]{cos(4x)} ?
The integral of sin(4x)\sqrt[3]{cos(4x)} is -3/16 cos^{4/3}(4x)+C