What is the integral of ((1-x)^3)/(x\sqrt[3]{x)} ?

The integral of ((1-x)^3)/(x\sqrt[3]{x)} is -3/(\sqrt[3]{x)}-9/2 x^{2/3}+9/5 x^{5/3}-3/8 x^{8/3}+C

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integral of ((1-x)^3)/(x\sqrt[3]{x)}

Solution steps

Expand

= \int \frac{1}{x ^{\frac{4}{3}}} - \frac{3}{x ^{\frac{1}{3}}} + 3 x^{\frac{2}{3}} - x^{\frac{5}{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 \frac{1}{x ^{\frac{4}{3}}} d x - \int \frac{3}{x ^{\frac{1}{3}}} d x + \int 3 x^{\frac{2}{3}} d x - \int x^{\frac{5}{3}} d x

\int \frac{3}{x ^{\frac{1}{3}}} d x = \frac{9}{2} x^{\frac{2}{3}}

\int 3 x^{\frac{2}{3}} d x = \frac{9}{5} x^{\frac{5}{3}}

\int x^{\frac{5}{3}} d x = \frac{3}{8} x^{\frac{8}{3}}

Add a constant to the solution

\frac{\partial}{\partial y} (x^{4} + 3 y^{3})

y = 3 x^{2} + 6 x + 6

\int (x - 1)^{2} d x

\int sin^{5} (\frac{x}{2}) cos^{4} (\frac{x}{2}) d x

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

What is the integral of ((1-x)^3)/(x\sqrt[3]{x)} ?
The integral of ((1-x)^3)/(x\sqrt[3]{x)} is -3/(\sqrt[3]{x)}-9/2 x^{2/3}+9/5 x^{5/3}-3/8 x^{8/3}+C