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

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

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

- \frac{3}{4} cos^{\frac{4}{3}} (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 the Power Rule

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

= - \frac{3}{4} u^{\frac{4}{3}}

Substitute back

u = cos (x)

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

Add a constant to the solution

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

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