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Integration problem. By parts I think.?
The problem is to evaluate the integral :
∫(x²/(x-1)) dx
I'm in calculus 2 and I believe the way to solve the problem is by using integration by parts; mainly because that's what we just learned. Haha. If you could help me solve it, not just give the answer I'd really appreciate it
1 Answer
- Anonymous1 decade agoFavorite Answer
∫ x²/(x - 1) dx
By long division, we have:
==> ∫ x + 1/(x - 1) + 1 dx
==> ∫ x dx + ∫ 1/(x - 1) dx + ∫ 1 dx
For the second integrand, let u = x - 1 and du = dx.
==> ∫ x dx + ∫ du/u + ∫ 1 dx
Then,
==> x²/2 + ln|u| + x + c
==> x²/2 + ln|x - 1| + x + c
I hope this helps!
Source(s): Knowledge