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

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

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

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

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

Solution steps

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

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

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

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

Add a constant to the solution

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

y^{^{'}} = (4 x + y)^{2}

\frac{\partial}{\partial x} (e^{x y} x)

\frac{d}{d x} (sin (x + \frac{π}{2}))

\int (x^{6} - 3 x^{2})^{4} (x^{5} - x) d x

\frac{d}{d t} (3 - 3 t)

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