Question

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

Answer 1

i can help

Answer 2

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

Answer 3

so you want to integrate this?

Answer 4

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

Answer 5

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

Answer 6

now use substitution:

\[u = x -1, x = u + 1, du=dx\]

Answer 7

now you go from trying to find the integral of

\[\int\limits_{}^{}(x^2 - x) / (x-1)^4 dx\]


to

\[\int\limits_{}^{} (u+1)/u^3 du\]

Answer 8

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