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

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

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

\frac{3}{4} sin^{\frac{4}{3}} (x) + C

Solution steps

Apply u-substitution

Apply the Power Rule

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

Substitute back

u = sin (x)

= \frac{3}{4} sin^{\frac{4}{3}} (x)

Add a constant to the solution

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

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