Help101
  • Help101
How do you integrate ((x^2)-x)/((x-1)^4)
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
i can help
anonymous
  • anonymous
\[(x^2 - x)/(x-1)^4\]
anonymous
  • anonymous
so you want to integrate this?

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anonymous
  • anonymous
the numerator can be viewed as \[(x^2-x) = x*(x-1)\]
anonymous
  • anonymous
so \[( x*(x-1) )/ ((x-1)^4) \]
anonymous
  • anonymous
now use substitution: \[u = x -1, x = u + 1, du=dx\]
anonymous
  • anonymous
now you go from trying to find the integral of \[\int\limits_{}^{}(x^2 - x) / (x-1)^4 dx\] to \[\int\limits_{}^{} (u+1)/u^3 du\]
anonymous
  • anonymous
so this one is easier, integrate this, then use the substitution relationship you established earlier and convert your solution to one in terms of x

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