Tìm nguyên hàm của hàm số sau: ∫(x−x√)(1+x√)/x√3dx

Question

\(\int \frac{\left(x\, -\, \sqrt{x} \right)\left(1\, +\, \sqrt{x} \right)}{\sqrt[{3}]{x} } \, {\rm d}x\)

Answer 1

\(\int \frac{\left(x\, -\, \sqrt{x} \right)\left(1\, +\, \sqrt{x} \right)}{\sqrt[{3}]{x} } \,  {\rm d}x\, =\, \int \frac{\, -\, \sqrt{x} \, +x\, \sqrt{x} }{\sqrt[{3}]{x} } \,  {\rm d}x=\, \int \left(-\, x^{\frac{1}{6} } \, +\, x^{\frac{7}{6} } \right)\,  {\rm d}x\)
\(=\, -\, \frac{6}{7} \, x^{\frac{7}{6} } \, +\, \frac{6}{13} x^{\frac{13}{6} } \, +\, C\, =\, -\, \frac{6}{7} \, x\, \sqrt[{6}]{x} \, +\, \frac{6}{13} x^{2} \, \sqrt[{6}]{x} \, +\, C.\)