What is the integral of (2x^4+2\sqrt[5]{x})/x ?

The integral of (2x^4+2\sqrt[5]{x})/x is (x^4)/2+10\sqrt[5]{x}+C

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integral of (2x^4+2\sqrt[5]{x})/x

Solution steps

Expand

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int \frac{2}{x ^{\frac{4}{5}}} d x = 10 x^{\frac{1}{5}}

= \frac{x ^{4}}{2} + 10 x^{\frac{1}{5}}

Apply radical rule:

Add a constant to the solution

What is the integral of (2x^4+2\sqrt[5]{x})/x ?
The integral of (2x^4+2\sqrt[5]{x})/x is (x^4)/2+10\sqrt[5]{x}+C