What is the integral of (8x-5)/(\sqrt[3]{x)} ?

The integral of (8x-5)/(\sqrt[3]{x)} is 24/5 x^{5/3}-15/2 x^{2/3}+C

integral of (8x-5)/(\sqrt[3]{x)}

\int \frac{8 x - 5}{3 x} d x

\frac{24}{5} x^{\frac{5}{3}} - \frac{15}{2} x^{\frac{2}{3}} + C

Solution steps

\int \frac{8 x - 5}{3 x} d x

Expand

\frac{8 x - 5}{3 x} : 8 x^{\frac{2}{3}} - \frac{5}{3 x}

= \int 8 x^{\frac{2}{3}} - \frac{5}{3 x} 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 8 x^{\frac{2}{3}} d x - \int \frac{5}{3 x} d x

\int 8 x^{\frac{2}{3}} d x = \frac{24}{5} x^{\frac{5}{3}}

\int \frac{5}{3 x} d x = \frac{15}{2} x^{\frac{2}{3}}

= \frac{24}{5} x^{\frac{5}{3}} - \frac{15}{2} x^{\frac{2}{3}}

Add a constant to the solution

= \frac{24}{5} x^{\frac{5}{3}} - \frac{15}{2} x^{\frac{2}{3}} + C

\frac{d}{d x} (\frac{sec ( 2 x )}{1 + tan ( 2 x )})

\int cot^{3} (\frac{x}{3}) d x

\int x ln^{4} (x) d x

\frac{\partial}{\partial x} (\frac{2 x - y}{5 x y + 6})

\frac{d}{d x} (\frac{7 + 2 ln ( x )}{x})

What is the integral of (8x-5)/(\sqrt[3]{x)} ?
The integral of (8x-5)/(\sqrt[3]{x)} is 24/5 x^{5/3}-15/2 x^{2/3}+C