Answer to Question #248519 in Calculus for Melky

Question #248519

  fraction numerator x squared plus x plus 1 over denominator x minus 1 end fraction



1
Expert's answer
2021-10-11T01:42:10-0400
"\\dfrac{x^2+x+1}{x-1}=\\dfrac{x^2-x+2x-2+3}{x-1}"

"=x+2+\\dfrac{3}{x-1}, x\\not=1"

"\\dfrac{x^2+x+1}{x-1}=x+2+\\dfrac{3}{x-1}, x\\not=1"



"\\int\\dfrac{x^2+x+1}{x-1}dx=\\int(x+2+\\dfrac{3}{x-1})dx"

"=\\dfrac{x^2}{2}+2x+3\\ln(|x-1|)+C"

"\\int\\dfrac{x^2+x+1}{x-1}dx=\\dfrac{x^2}{2}+2x+3\\ln(|x-1|)+C"


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