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

The integral of (sin(x))/(\sqrt[3]{cos(x))} is -3/2 cos^{2/3}(x)+C

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

- \frac{3}{2} cos^{\frac{2}{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}{2} u^{\frac{2}{3}}

= - \frac{3}{2} u^{\frac{2}{3}}

Substitute back

u = cos (x)

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

Add a constant to the solution

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

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\int \frac{2}{3} e^{- 2 x} d x

What is the integral of (sin(x))/(\sqrt[3]{cos(x))} ?
The integral of (sin(x))/(\sqrt[3]{cos(x))} is -3/2 cos^{2/3}(x)+C