What is the integral of 1/x (\sqrt[6]{x^5}) ?

The integral of 1/x (\sqrt[6]{x^5}) is 6/5 x^{5/6}+C

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integral of 1/x (\sqrt[6]{x^5})

\frac{6}{5} x^{\frac{5}{6}} + C

Solution steps

assuming

x \geq 0

= \int \frac{1}{x} x^{\frac{5}{6}} d x

Simplify

\frac{1}{x} x^{\frac{5}{6}} : \frac{1}{x ^{\frac{1}{6}}}

= \int \frac{1}{x ^{\frac{1}{6}}} d x

Apply the Power Rule

: \frac{6}{5} x^{\frac{5}{6}}

= \frac{6}{5} x^{\frac{5}{6}}

Add a constant to the solution

= \frac{6}{5} x^{\frac{5}{6}} + C

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What is the integral of 1/x (\sqrt[6]{x^5}) ?
The integral of 1/x (\sqrt[6]{x^5}) is 6/5 x^{5/6}+C