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

The integral of (3+x^5)/(\sqrt[5]{x)} is 15/4 x^{4/5}+5/29 x^{29/5}+C

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

\frac{15}{4} x^{\frac{4}{5}} + \frac{5}{29} x^{\frac{29}{5}} + C

Solution steps

Expand

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

\int x^{\frac{24}{5}} d x = \frac{5}{29} x^{\frac{29}{5}}

= \frac{15}{4} x^{\frac{4}{5}} + \frac{5}{29} x^{\frac{29}{5}}

Add a constant to the solution

= \frac{15}{4} x^{\frac{4}{5}} + \frac{5}{29} x^{\frac{29}{5}} + C

What is the integral of (3+x^5)/(\sqrt[5]{x)} ?
The integral of (3+x^5)/(\sqrt[5]{x)} is 15/4 x^{4/5}+5/29 x^{29/5}+C