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

The integral of (x-x^2)/(2\sqrt[3]{x)} is 1/2 (3/5 x^{5/3}-3/8 x^{8/3})+C

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integral of (x-x^2)/(2\sqrt[3]{x)}

\frac{1}{2} (\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{8} x^{\frac{8}{3}}) + C

Solution steps

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{8} x^{\frac{8}{3}})

Add a constant to the solution

= \frac{1}{2} (\frac{3}{5} x^{\frac{5}{3}} - \frac{3}{8} x^{\frac{8}{3}}) + C

What is the integral of (x-x^2)/(2\sqrt[3]{x)} ?
The integral of (x-x^2)/(2\sqrt[3]{x)} is 1/2 (3/5 x^{5/3}-3/8 x^{8/3})+C