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

The integral of sqrt(x^3)+\sqrt[3]{x^2} is 2/5 x^{5/2}+3/5 x^{5/3}+C

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integral of sqrt(x^3)+\sqrt[3]{x^2}

\frac{2}{5} x^{\frac{5}{2}} + \frac{3}{5} x^{\frac{5}{3}} + 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

\int x^{3} d x = \frac{2}{5} x^{\frac{5}{2}}

= \frac{2}{5} x^{\frac{5}{2}} + \frac{3}{5} x^{\frac{5}{3}}

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} + \frac{3}{5} x^{\frac{5}{3}} + C

y^{^{''}} - 4 y^{^{'}} + 4 y = 5 t^{- 1} e^{2 t}

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

\frac{\partial}{\partial x} (x^{2} (x - y)^{- 2})

\frac{d}{d x} (\frac{1}{3 ( x + 2 ) ^{\frac{2}{3}}})

f (x) = (2 x^{2} + 1)

What is the integral of sqrt(x^3)+\sqrt[3]{x^2} ?
The integral of sqrt(x^3)+\sqrt[3]{x^2} is 2/5 x^{5/2}+3/5 x^{5/3}+C