I'm sure it's pretty simple, but I'm just not seeing it.(adsbygoogle = window.adsbygoogle || []).push({});

Integrate (x^2/(x-1)) dx

I did it with a u substitution, letting u = x-1 and then x = u+1

which ultimately leads me to integrate (u^2/u) + (2u/u) + (1/u)

After canceling, integrating, and substituting I'm left with

(x^2/2) + x + ln(abs)(x-1) + C (I assume I'm alright rolling the -3/2 that I had left over into C to make it match the book answer?)

The book does it like this and I'm not sure what's going on

Integrate (x^2/(x-1)) dx = Integrate (x+1) dx + Integrate (1/(x-1)) dx

I think they are splitting it up somehow, hence the 1/x-1, but I'm not sure how they got to x+1

which yields the same answer I had.

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# Homework Help: How did the book do this integration

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