Mathematics 34 Online
OpenStudy (help101):

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

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 $( x*(x-1) )/ ((x-1)^4)$

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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