What is the integral of (\sqrt[9]{x^2}-3/(x^2)) ?

The integral of (\sqrt[9]{x^2}-3/(x^2)) is 9/11 x^{11/9}+3/x+C

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integral of (\sqrt[9]{x^2}-3/(x^2))

\frac{9}{11} x^{\frac{11}{9}} + \frac{3}{x} + C

Solution steps

assuming

x \geq 0

= \int x^{\frac{2}{9}} - \frac{3}{x ^{2}} 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 x^{\frac{2}{9}} d x - \int \frac{3}{x ^{2}} d x

\int x^{\frac{2}{9}} d x = \frac{9}{11} x^{\frac{11}{9}}

\int \frac{3}{x ^{2}} d x = - \frac{3}{x}

= \frac{9}{11} x^{\frac{11}{9}} - (- \frac{3}{x})

Simplify

= \frac{9}{11} x^{\frac{11}{9}} + \frac{3}{x}

Add a constant to the solution

= \frac{9}{11} x^{\frac{11}{9}} + \frac{3}{x} + C

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What is the integral of (\sqrt[9]{x^2}-3/(x^2)) ?
The integral of (\sqrt[9]{x^2}-3/(x^2)) is 9/11 x^{11/9}+3/x+C