What is the integral of \sqrt[9]{x^2}+xsqrt(x) ?

The integral of \sqrt[9]{x^2}+xsqrt(x) is 9/11 x^{11/9}+2/5 x^{5/2}+C

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integral of \sqrt[9]{x^2}+xsqrt(x)

\frac{9}{11} x^{\frac{11}{9}} + \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

assuming

x \geq 0

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

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

\int x x d x = \frac{2}{5} x^{\frac{5}{2}}

= \frac{9}{11} x^{\frac{11}{9}} + \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{9}{11} x^{\frac{11}{9}} + \frac{2}{5} x^{\frac{5}{2}} + C

y = x^{2} - x + 7

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

\int_{0}^{l n (5)} e^{x} - e^{- 3 x} d x

\frac{x}{4 x + 6}

\frac{\partial}{\partial x} (x y + \frac{4}{x} + \frac{2}{y})

What is the integral of \sqrt[9]{x^2}+xsqrt(x) ?
The integral of \sqrt[9]{x^2}+xsqrt(x) is 9/11 x^{11/9}+2/5 x^{5/2}+C