What is the integral of (11x^3-1)/(\sqrt[3]{x)} ?

The integral of (11x^3-1)/(\sqrt[3]{x)} is 3x^{11/3}-3/2 x^{2/3}+C

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integral of (11x^3-1)/(\sqrt[3]{x)}

3 x^{\frac{11}{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 11 x^{\frac{8}{3}} d x = 3 x^{\frac{11}{3}}

= 3 x^{\frac{11}{3}} - \frac{3}{2} x^{\frac{2}{3}}

Add a constant to the solution

= 3 x^{\frac{11}{3}} - \frac{3}{2} x^{\frac{2}{3}} + C

\frac{d y}{d x} = 3 - 0.0003 y

\frac{d}{d x} (3 x^{2} - 6 x + 5)

\int (\frac{1}{y} - 1) d y

y^{^{''}} + 4 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y^{^{'}} = x + y, y (0) = 9

What is the integral of (11x^3-1)/(\sqrt[3]{x)} ?
The integral of (11x^3-1)/(\sqrt[3]{x)} is 3x^{11/3}-3/2 x^{2/3}+C