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

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

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

Solution steps

Apply Integration By Parts

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

Apply radical rule:

Add a constant to the solution

\int \frac{3 ^{2 x}}{1 + 3 ^{2 x}} d x

x \to \infty lim (tan (\frac{7}{x}))

\frac{d}{d x} (6 x^{2} + 15 x y + 3 y^{2})

\int (e^{x} x) d x

x \to \infty lim (\frac{( e ^{2 x} - 8 - 19 x )}{( 19 x ) ^{2}})

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