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

The integral of \sqrt[6]{x}+1/(\sqrt[6]{x)} is 6/7 x^{7/6}+6/5 x^{5/6}+C

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

\frac{6}{7} x^{\frac{7}{6}} + \frac{6}{5} x^{\frac{5}{6}} + C

Solution steps

Apply the Sum Rule:

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

= \frac{6}{7} x^{\frac{7}{6}} + \frac{6}{5} x^{\frac{5}{6}}

Add a constant to the solution

= \frac{6}{7} x^{\frac{7}{6}} + \frac{6}{5} x^{\frac{5}{6}} + C

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What is the integral of \sqrt[6]{x}+1/(\sqrt[6]{x)} ?
The integral of \sqrt[6]{x}+1/(\sqrt[6]{x)} is 6/7 x^{7/6}+6/5 x^{5/6}+C