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

\int 10 t d t

f (x) = (t^{6} + 1)^{500}

2 x \frac{d y}{d x} = 2 x e^{x} - 2 y + 6 x^{2}

\int \frac{1}{3 - 8 x} d x

- \frac{x}{( 25 - x ^{2} ) ^{\frac{1}{2}}}

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