Integrate (2x)/((x-1)^3)?
I'm trying to find the integral of (2x)/((x-1)^3). Can anyone help me step by step on what to do? I was looking at the answer on WolframAlpha and I'm very confused on their use of partial fractions. Thank you!
More Questions From This User See All
Answers & Comments
Verified answer
If you sub u=(x-1) you get 2(u+1)/u^3 = 2u/u^3+2/u^3=2/u^2+2/u^3 so the PFs are
2/(x-1)^2+2/(x-1)^3 which you should be able to integrate to get -2/(x-1)-1/(x-1)^2+C.
If you are familiar with integration by substitution then you get the
integral of (2/u^2 +2/u^3)du which is comparatively easy.