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

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

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

y^{^{'}} = 2 y^{2} + x y^{2}

11 y^{^{''}} + 13 y^{^{'}} + \frac{13}{44} y = 0, y (0) = 2, y^{^{'}} (0) = 1

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

x^{\frac{2}{x}}

x \to 0 lim (\frac{5 x + x ^{2}}{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