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

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

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integral of \sqrt[3]{sin(θ)}cos(θ)

\frac{3}{4} sin^{\frac{4}{3}} (θ) + C

Solution steps

Apply u-substitution

Apply the Power Rule

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

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

Substitute back

u = sin (θ)

= \frac{3}{4} sin^{\frac{4}{3}} (θ)

Add a constant to the solution

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

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