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

The integral of \sqrt[3]{3x^2} is \sqrt[3]{3}x^{5/3}-(2\sqrt[3]{3})/5 x^{5/3}+C

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

\int 3 3 x^{2} d x

33 x^{\frac{5}{3}} - \frac{2 3 3}{5} x^{\frac{5}{3}} + C

Solution steps

\int 3 3 x^{2} d x

Apply Integration By Parts

= 33 x 3 x^{2} - \int \frac{2 x ^{2}}{3 ^{\frac{2}{3}} ( x ^{2} ) ^{\frac{2}{3}}} d x

\int \frac{2 x ^{2}}{3 ^{\frac{2}{3}} ( x ^{2} ) ^{\frac{2}{3}}} d x = \frac{2 \cdot 3 ^{\frac{1}{3}}}{5} x^{\frac{5}{3}}

= 33 x 3 x^{2} - \frac{2 \cdot 3 ^{\frac{1}{3}}}{5} x^{\frac{5}{3}}

Simplify

33 x 3 x^{2} - \frac{2 \cdot 3 ^{\frac{1}{3}}}{5} x^{\frac{5}{3}} : 33 x^{\frac{5}{3}} - \frac{2 3 3}{5} x^{\frac{5}{3}}

= 33 x^{\frac{5}{3}} - \frac{2 3 3}{5} x^{\frac{5}{3}}

Add a constant to the solution

= 33 x^{\frac{5}{3}} - \frac{2 3 3}{5} x^{\frac{5}{3}} + C

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What is the integral of \sqrt[3]{3x^2} ?
The integral of \sqrt[3]{3x^2} is \sqrt[3]{3}x^{5/3}-(2\sqrt[3]{3})/5 x^{5/3}+C