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

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

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

\frac{3}{8} x^{\frac{8}{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 x^{\frac{5}{3}} d x = \frac{3}{8} x^{\frac{8}{3}}

= \frac{3}{8} x^{\frac{8}{3}} + \frac{3}{2} x^{\frac{2}{3}}

Add a constant to the solution

= \frac{3}{8} x^{\frac{8}{3}} + \frac{3}{2} x^{\frac{2}{3}} + C

x \to 0 + lim (1 - \frac{1}{x})

\frac{d y}{d x}, x^{3} - 3 x^{2} y + 2 x y^{2} = 12

x^{2} (1 - 6 x)

\frac{x}{( x ^{2} + 5 x + 6 )}, 0, 1

\int e^{- θ x} d x

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