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Integral of (x^2+1)/(x^(1/3))

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$\frac{3}{8}\sqrt[3]{x^{8}}+\frac{3}{2}\sqrt[3]{x^{2}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{x^2+1}{x^{\frac{1}{3}}}dx$
1

Split the fraction $\frac{x^2+1}{\sqrt[3]{x}}$ in two terms with same denominator

$\int\left(\frac{x^2}{\sqrt[3]{x}}+\frac{1}{\sqrt[3]{x}}\right)dx$

$\frac{3}{8}\sqrt[3]{x^{8}}+\frac{3}{2}\sqrt[3]{x^{2}}+C_0$

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$\int\frac{x^2+1}{x^{\frac{1}{3}}}dx$

Main topic:

Integral calculus

~ 0.63 seconds