Question

Nesse exercício resolvido de integral, gostaria de saber como surgiu aquele 6.

Answer 1

$\sqrt[5]{x} = x^{\frac{1}{5} } \\\\Entao,\\\\\\int\limits^a_b {x^{\frac{1}{5} } } \, dx = \frac{5}{6}.x^{\frac{1}{5}+ 1 } = \frac{5}{6}.x^{\frac{5}{6} }  \\  \\Como x^{\frac{1}{2} } = \sqrt[2]{x^{1} }, fica:\\  \\\frac{5}{6}.x^{\frac{5}{6} } = \frac{5}{6}.\sqrt[5]{x^{6} }  }$

Answer 2

Veio dessa integral

$\int \sqrt[5]{x}dx = \int x^{\frac{1}{5}}dx = \dfrac{x^{\frac{1}{5}+1}}{\frac{1}{5}+1} = \dfrac{x^{\frac{6}{5}}}{\frac{6}{5}}=\dfrac{5}{6}x^{\frac{5}{6}}=\dfrac{5}{6}\cdot \sqrt[5]{x^6}$