What is the integral of \sqrt[3]{1+sin(x)}cos(x) ?

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

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integral of \sqrt[3]{1+sin(x)}cos(x)

\int 3 1 + sin (x) cos (x) d x

\frac{3}{4} (1 + sin (x))^{\frac{4}{3}} + C

Solution steps

\int 3 1 + sin (x) cos (x) d x

Apply u-substitution

= \int 3 1 + u d u

Apply u-substitution

= \int 3 v d v

Apply the Power Rule

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

Substitute back

= \frac{3}{4} (1 + sin (x))^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{4} (1 + sin (x))^{\frac{4}{3}} + C

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