What is the integral of \sqrt[7]{x}+\sqrt[8]{x} ?

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

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integral of \sqrt[7]{x}+\sqrt[8]{x}

\int 7 x + 8 x d x

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

Solution steps

\int 7 x + 8 x d x

Apply the Sum Rule:

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

= \int 7 x d x + \int 8 x d x

\int 7 x d x = \frac{7}{8} x^{\frac{8}{7}}

\int 8 x d x = \frac{8}{9} x^{\frac{9}{8}}

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

Add a constant to the solution

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

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