Question

Qual a integral de x^-1/3 - 5/x*dx

Answer 1

Boa noite Silene!

Solução!

$\displaystyle \int( x^{ -\frac{1}{3} }- \frac{5}{x})dx\\\\\\\\\\\ \displaystyle \int( x^{ -\frac{1}{3} })dx - 5\displaystyle \int \frac{1}{x})dx\\\\\\\\\\ \left ( \dfrac{ x^{ -\frac{1}{3}+1 } }{- \frac{1}{3} +1}\right ) -5\left ( \dfrac{ 1 }{x} \right )\\\\\\\\\ \left ( \dfrac{ x^{\frac{2}{3} } }{\frac{2}{3}}\right ) -5ln(x)\\\\\\\\\ ( \frac{3}{2} \sqrt[3]{ x^{2} } }{}\right ) -5ln(x)+c)$


$\boxed{Resposta:\displaystyle \int( x^{ -\frac{1}{3}} - \frac{5}{x})dx=( \frac{3}{2} \sqrt[3]{ x^{2} } -5ln(x)+c) }$

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Bons estudos!