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

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

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

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

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

Solution steps

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

Simplify

\frac{3 x}{x ^{3}} : \frac{1}{x ^{\frac{8}{3}}}

= \int \frac{1}{x ^{\frac{8}{3}}} d x

Apply the Power Rule

: - \frac{3}{5 x ^{\frac{5}{3}}}

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

Add a constant to the solution

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

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