What is the integral of \sqrt[8]{x}+1/(\sqrt[8]{x)} ?

The integral of \sqrt[8]{x}+1/(\sqrt[8]{x)} is 8/9 x^{9/8}+8/7 x^{7/8}+C

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integral of \sqrt[8]{x}+1/(\sqrt[8]{x)}

\frac{8}{9} x^{\frac{9}{8}} + \frac{8}{7} x^{\frac{7}{8}} + 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{8}{9} x^{\frac{9}{8}} + \frac{8}{7} x^{\frac{7}{8}}

Add a constant to the solution

= \frac{8}{9} x^{\frac{9}{8}} + \frac{8}{7} x^{\frac{7}{8}} + C

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What is the integral of \sqrt[8]{x}+1/(\sqrt[8]{x)} ?
The integral of \sqrt[8]{x}+1/(\sqrt[8]{x)} is 8/9 x^{9/8}+8/7 x^{7/8}+C