What is the integral of (2x^2+4x^4-1)/(\sqrt[3]{x)} ?

The integral of (2x^2+4x^4-1)/(\sqrt[3]{x)} is 3/4 x^{8/3}+6/7 x^{14/3}-3/2 x^{2/3}+C

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integral of (2x^2+4x^4-1)/(\sqrt[3]{x)}

\frac{3}{4} x^{\frac{8}{3}} + \frac{6}{7} x^{\frac{14}{3}} - \frac{3}{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 2 x^{\frac{5}{3}} d x = \frac{3}{4} x^{\frac{8}{3}}

\int 4 x^{\frac{11}{3}} d x = \frac{6}{7} x^{\frac{14}{3}}

= \frac{3}{4} x^{\frac{8}{3}} + \frac{6}{7} x^{\frac{14}{3}} - \frac{3}{2} x^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{4} x^{\frac{8}{3}} + \frac{6}{7} x^{\frac{14}{3}} - \frac{3}{2} x^{\frac{2}{3}} + C

What is the integral of (2x^2+4x^4-1)/(\sqrt[3]{x)} ?
The integral of (2x^2+4x^4-1)/(\sqrt[3]{x)} is 3/4 x^{8/3}+6/7 x^{14/3}-3/2 x^{2/3}+C