What is the integral of sin^{1/3}(x)cos(x) ?

The integral of sin^{1/3}(x)cos(x) is 3/4 sin^{4/3}(x)+C

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integral of sin^{1/3}(x)cos(x)

\int sin^{\frac{1}{3}} (x) cos (x) d x

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

Solution steps

\int 3 sin (x) cos (x) d x

Apply u-substitution

: \int 3 u d u

= \int 3 u d u

Apply the Power Rule

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

= \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

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What is the integral of sin^{1/3}(x)cos(x) ?
The integral of sin^{1/3}(x)cos(x) is 3/4 sin^{4/3}(x)+C