What is the integral of (x^{1/2}+5)/(\sqrt[3]{x)} ?

The integral of (x^{1/2}+5)/(\sqrt[3]{x)} is 6/7 x^{7/6}+15/2 x^{2/3}+C

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integral of (x^{1/2}+5)/(\sqrt[3]{x)}

\frac{6}{7} x^{\frac{7}{6}} + \frac{15}{2} x^{\frac{2}{3}} + 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{1}{6}} d x = \frac{6}{7} x^{\frac{7}{6}}

= \frac{6}{7} x^{\frac{7}{6}} + \frac{15}{2} x^{\frac{2}{3}}

Add a constant to the solution

= \frac{6}{7} x^{\frac{7}{6}} + \frac{15}{2} x^{\frac{2}{3}} + C

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What is the integral of (x^{1/2}+5)/(\sqrt[3]{x)} ?
The integral of (x^{1/2}+5)/(\sqrt[3]{x)} is 6/7 x^{7/6}+15/2 x^{2/3}+C