What is the integral of x^2*\sqrt[3]{x} ?

The integral of x^2*\sqrt[3]{x} is 1/3 x^3\sqrt[3]{x}-1/30 x^{10/3}+C

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integral of x^2*\sqrt[3]{x}

\int x^{2} \cdot 3 x d x

\frac{1}{3} x^{3} 3 x - \frac{1}{30} x^{\frac{10}{3}} + C

Solution steps

\int x^{2} 3 x d x

Apply Integration By Parts

: \frac{1}{3} x^{3} 3 x - \int \frac{1}{9} x^{\frac{7}{3}} d x

= \frac{1}{3} x^{3} 3 x - \int \frac{1}{9} x^{\frac{7}{3}} d x

\int \frac{1}{9} x^{\frac{7}{3}} d x = \frac{1}{30} x^{\frac{10}{3}}

= \frac{1}{3} x^{3} 3 x - \frac{1}{30} x^{\frac{10}{3}}

Add a constant to the solution

= \frac{1}{3} x^{3} 3 x - \frac{1}{30} x^{\frac{10}{3}} + C

- e^{- x}

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What is the integral of x^2*\sqrt[3]{x} ?
The integral of x^2*\sqrt[3]{x} is 1/3 x^3\sqrt[3]{x}-1/30 x^{10/3}+C