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Popular >

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

Solution

Solution

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

Popular Examples

derivative of 2(3-8x^3)

\frac{d}{d x} (2 (3 - 8 x)^{3})

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\frac{d}{d x} ((4 x^{2} - 8 x + 8) e^{x})

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\int \frac{1}{( x - 8 ) ( x ^{2} + 25 )} d x

integral of 2x(x^2+1)^9

\int 2 x (x^{2} + 1)^{9} d x

Frequently Asked Questions (FAQ)

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