Question

Resolva a integral por frações parciais.
#SOS

Answer 1

Resposta:

OLÁ

VAMOS A SUA PERGUNTA:⇒⇒

$\sf \displaystyle\int\dfrac{-2x+4}{x^4-2x^3+2x^2-2x+1}~dx$

$\sf =\displaystyle\int-\dfrac{2}{x-1} ~+\dfrac{1}{(x-1)^2}~ + \dfrac{2x+1}{x^2+1} ~dx$

$\sf =-\displaystyle\int-\dfrac{2}{x-1} ~dx+\displaystyle\int\dfrac{1}{(x-1)}~ dx+ \displaystyle\int\dfrac{2x+1}{x^2+1} ~dx$

$\sf \displaystyle\int\dfrac{2}{x-1}~dx=2in|x-1|$

$\sf \displaystyle\int\dfrac{2}{(x-1)^2}~dx=-\dfrac{1}{x-1}$

$\sf \displaystyle\int\dfrac{2x+1}{x^2+1}~dx=in|x^2+1|+arctan(x)$

$\sf =-2in|x-1|-\dfrac{1}{x-1}+in|x^2+1|+arctan(x)$

$\boxed{\bold{\displaystyle{\clubsuit\ \spadesuit\ \maltese\ \sf \red{=-2in|x-1|-\dfrac{1}{x-1}+in|x^2+1|+arctan(x)+C} }}}\ \checkmark$← RESPOSTA.

Explicação passo-a-passo:

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