Question

Qual a integral de x^5+2x²-1*dx/x^4

Answer 1

Boa noite Silene!

Solução!

$\displaystyle \int\frac{( x^{5} +2 x^{2} -1)}{x^{4}}dx\\\\\\\\\\ \displaystyle \int\left (\frac{x^{5}}{x^{4}} + \frac{2 x^{2} }{ x^{4} }+ \frac{-1}{ x^{4} } \right )dx\\\\\\\\\ \displaystyle \int( x^{5}. x^{-4}+2 x^{2} . x^{-4}-1. x^{-4})dx \\\\\\\\ \displaystyle \int( x+2 x^{-2}- x^{-4})dx \\\\\\\\ Agora~~vamos~~integrar!$


$\left( \dfrac{ x^{1+1} }{1+1} +\dfrac{2 x^{-2+1} }{-2+1} - \dfrac{ x^{-4+1} }{-4+1}\right ) \\\\\\\\\ \left( \dfrac{ x^{2} }{2} +\dfrac{2 x^{-1} }{-1} - \dfrac{ x^{-3} }{-3}\right ) \\\\\\\\\ \left( \dfrac{ x^{2} }{2} -\dfrac{2 }{ x } + \dfrac{1 }{3x^{3}}+c\right )$


$\boxed{Resposta:\displaystyle \int\frac{( x^{5} +2 x^{2} -1)}{x^{4}}dx =\left( \dfrac{ x^{2} }{2} -\dfrac{2 }{ x } + \dfrac{1 }{3x^{3}}+c\right )}$

Boa noite!
Bons estudos!