cherrilyn
  • cherrilyn
use long division to write f(x) as the sum of a polynomial and a proper rational function. Then calculate the integral of f(x)d(x). EQUATION: f(x) = x^3-1 / x^2-x. I did long division and got -x-1 = A(x-1) + B(x) and so x = 1 and x = 0. What should I do next?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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amistre64
  • amistre64
when I do the division i end up with: x + 1 + (1/x)
amistre64
  • amistre64
then you intergrate the seperate terms: x^2/2 +x +ln(x) +C
cherrilyn
  • cherrilyn
x^2 -x goes into x^3 - 1 x times with a remainder of -x-1 right?

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amistre64
  • amistre64
x +1 + (x-1)/x(x-1) -------------- x^2 -x | x^3 -1 -x^3 +x^2 ----------- x^2 -1 -x^2+x --------- x-1
amistre64
  • amistre64
remember to "subtract" the result :)
amistre64
  • amistre64
[S] x + 1 + (1/x) dx (x^2)/2 +x +ln(x) +C
cherrilyn
  • cherrilyn
ooooooh Wow okay! Thanks!

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