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

The integral of x*\sqrt[3]{x} is 1/2 x^2\sqrt[3]{x}-1/14 x^{7/3}+C

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

Solution steps

Apply Integration By Parts

\int \frac{1}{6} x^{\frac{4}{3}} d x = \frac{1}{14} x^{\frac{7}{3}}

Add a constant to the solution

\int x^{3} \frac{1}{x} d x

\int \frac{4}{x ^{2} + 3} d x

\int (x^{\frac{3}{2}} - 2 x^{3} + x) d x

\int sin (x) (3 x^{2} + x - 1) d x

\int 3 x^{2} 5^{4 x} d x

What is the integral of x*\sqrt[3]{x} ?
The integral of x*\sqrt[3]{x} is 1/2 x^2\sqrt[3]{x}-1/14 x^{7/3}+C