What is the integral of (sqrt(x)+4)/(\sqrt[3]{x)} ?

The integral of (sqrt(x)+4)/(\sqrt[3]{x)} is 6/7 x^{7/6}+6x^{2/3}+C

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integral of (sqrt(x)+4)/(\sqrt[3]{x)}

\frac{6}{7} x^{\frac{7}{6}} + 6 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

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

Add a constant to the solution

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

\frac{d}{d x} (x^{3} - x^{2} - 6 x + 2)

\frac{d}{d x} (2 + 3 (x - 1) + 3 (x - 1)^{2} + d (x - 1)^{3})

\frac{d}{d x} (\frac{1}{x + 2} - 1)

\int cos^{3} (2 x) sin^{2} (2 x) d x

\frac{d}{d x} (\frac{1}{lo g _{4} ( x )})

What is the integral of (sqrt(x)+4)/(\sqrt[3]{x)} ?
The integral of (sqrt(x)+4)/(\sqrt[3]{x)} is 6/7 x^{7/6}+6x^{2/3}+C