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)}

\int 9 x + \frac{1}{9 x} d x

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

Solution steps

\int 9 x + \frac{1}{9 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 9 x d x + \int \frac{1}{9 x} d x

\int 9 x d x = \frac{9}{10} x^{\frac{10}{9}}

\int \frac{1}{9 x} d x = \frac{9}{8} x^{\frac{8}{9}}

= \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

\frac{d ^{2} y}{d x ^{2}} - 4 y = 0, y (0) = 2

\frac{d}{d x} (ln (e^{4 x}))

\frac{d}{d y} (y cos (x - y))

y = x^{3} + 6

\frac{s}{( s + 1 ) ( s + 2 )}

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