Question

Calcule as integrais usando fracões parciais

Answer 1

Caso tenha problemas para visualizar resposta experimente abrir pelo navegador

https://brainly.com.br/tarefa/33822072?utm_source=android&utm_medium=share&utm_campaign=question

=======================================

$\sf{\dfrac{x+4}{x^2+5x-6}=\dfrac{x+4}{(x-1)(x+6)}=\dfrac{A}{x-1}+\dfrac{B}{x+6}}$

$\sf{A=\dfrac{x+4}{x+6}\Bigg|_{x=1}=\dfrac{5}{7}}\\\sf{B=\dfrac{x+4}{x-1}\Bigg|_{x=-6}=\dfrac{2}{7}}$

$\displaystyle\sf{\int\dfrac{x+4}{x^2+5x-6}~dx=\dfrac{5}{7}\int\dfrac{dx}{x-1}+\dfrac{2}{7}\int\dfrac{dx}{x+6}}\\\sf{\dfrac{5}{7}\ell n|x-1|+\dfrac{2}{7}\ell n|x+6|+k}$

$\displaystyle\sf{\int\dfrac{x+4}{x^2+5x-6}~dx=\ell n\left|([x-1]^5\cdot[x+6]^2)^{\frac{1}{7}}\right|+k}$