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

The integral of ((sqrt(x)-\sqrt[3]{x})/x)^2 is ln|x|+(12)/(\sqrt[6]{x)}-3/(\sqrt[3]{x)}+C

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

Solution steps

Expand

= \int \frac{1}{x} - \frac{2}{x ^{\frac{7}{6}}} + \frac{1}{x ^{\frac{4}{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} d x - \int \frac{2}{x ^{\frac{7}{6}}} d x + \int \frac{1}{x ^{\frac{4}{3}}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

Simplify

Add a constant to the solution

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What is the integral of ((sqrt(x)-\sqrt[3]{x})/x)^2 ?
The integral of ((sqrt(x)-\sqrt[3]{x})/x)^2 is ln|x|+(12)/(\sqrt[6]{x)}-3/(\sqrt[3]{x)}+C