What is the integral of \sqrt[3]{x}-1/(\sqrt[3]{x)} ?

The integral of \sqrt[3]{x}-1/(\sqrt[3]{x)} is 3/4 x^{4/3}-3/2 x^{2/3}+C

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integral of \sqrt[3]{x}-1/(\sqrt[3]{x)}

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

\frac{3}{4} x^{\frac{4}{3}} - \frac{3}{2} x^{\frac{2}{3}} + C

Solution steps

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

Apply the Sum Rule:

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

= \int 3 x d x - \int \frac{1}{3 x} d x

\int 3 x d x = \frac{3}{4} x^{\frac{4}{3}}

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

= \frac{3}{4} x^{\frac{4}{3}} - \frac{3}{2} x^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{4} x^{\frac{4}{3}} - \frac{3}{2} x^{\frac{2}{3}} + C

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What is the integral of \sqrt[3]{x}-1/(\sqrt[3]{x)} ?
The integral of \sqrt[3]{x}-1/(\sqrt[3]{x)} is 3/4 x^{4/3}-3/2 x^{2/3}+C