What is the integral of \sqrt[8]{x}+\sqrt[9]{x} ?

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

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integral of \sqrt[8]{x}+\sqrt[9]{x}

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

Add a constant to the solution

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

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