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OpenStudy (help101):

How do you integrate ((x^2)-x)/((x-1)^4)

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OpenStudy (anonymous):

i can help

OpenStudy (anonymous):

\[(x^2 - x)/(x-1)^4\]

OpenStudy (anonymous):

so you want to integrate this?

OpenStudy (anonymous):

the numerator can be viewed as \[(x^2-x) = x*(x-1)\]

OpenStudy (anonymous):

so \[( x*(x-1) )/ ((x-1)^4) \]

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OpenStudy (anonymous):

now use substitution: \[u = x -1, x = u + 1, du=dx\]

OpenStudy (anonymous):

now you go from trying to find the integral of \[\int\limits_{}^{}(x^2 - x) / (x-1)^4 dx\] to \[\int\limits_{}^{} (u+1)/u^3 du\]

OpenStudy (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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