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

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

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integral of (5+\sqrt[3]{x})/x

Solution steps

Expand

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ + 3 x^{\frac{1}{3}}

Apply radical rule:

Add a constant to the solution

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