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

The integral of \sqrt[5]{x}+1/(\sqrt[5]{x)} is 5/6 x^{6/5}+5/4 x^{4/5}+C

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

\frac{5}{6} x^{\frac{6}{5}} + \frac{5}{4} x^{\frac{4}{5}} + 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{5}{6} x^{\frac{6}{5}} + \frac{5}{4} x^{\frac{4}{5}}

Add a constant to the solution

= \frac{5}{6} x^{\frac{6}{5}} + \frac{5}{4} x^{\frac{4}{5}} + C

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What is the integral of \sqrt[5]{x}+1/(\sqrt[5]{x)} ?
The integral of \sqrt[5]{x}+1/(\sqrt[5]{x)} is 5/6 x^{6/5}+5/4 x^{4/5}+C