What is the integral of \sqrt[9]{x}+1/(\sqrt[9]{x)} ?

The integral of \sqrt[9]{x}+1/(\sqrt[9]{x)} is 9/10 x^{10/9}+9/8 x^{8/9}+C

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integral of \sqrt[9]{x}+1/(\sqrt[9]{x)}

\frac{9}{10} x^{\frac{10}{9}} + \frac{9}{8} x^{\frac{8}{9}} + 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{9}{10} x^{\frac{10}{9}} + \frac{9}{8} x^{\frac{8}{9}}

Add a constant to the solution

= \frac{9}{10} x^{\frac{10}{9}} + \frac{9}{8} x^{\frac{8}{9}} + C

What is the integral of \sqrt[9]{x}+1/(\sqrt[9]{x)} ?
The integral of \sqrt[9]{x}+1/(\sqrt[9]{x)} is 9/10 x^{10/9}+9/8 x^{8/9}+C