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

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

Answer

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

Step-by-step explanation

Problem

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

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

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

Unlock this step-by-step solution!

Answer

$\frac{3}{2}\sqrt[3]{x^{2}}+\frac{3}{8}\sqrt[3]{x^{8}}+C_0$
$\int\frac{x^2+1}{x^{\frac{1}{3}}}dx$

Main topic:

Integral calculus

Used formulas:

1. See formulas

Time to solve it:

0.34 seconds