## cherrilyn 5 years ago evaluate the integral

1. cherrilyn

$\int\limits_{?}^{?}(x ^{2}-x+1) dx/ x ^{2}-x$

2. anonymous

You have to give us a hint. Which part of the book are you at?

3. cherrilyn

hehe. partial functions

4. anonymous

$LHS =A/(X-1) +B(x+1)$

5. anonymous

B/(x+1)

6. cherrilyn

umm.... wouldn't it be Ax+B/x^2+x? or are you skipping steps

7. anonymous

Oh, I haven't done these in a while, may be you should start it.

8. anonymous

Oh, the bottom is not the difference of two squares, I misread it.

9. cherrilyn

can you only use long division if the denominator is the difference of two squares?

10. anonymous

$LHS =A/x + B/(x-1)$

11. cherrilyn

are you sure?

12. anonymous

$x ^{2}-x=x(x-1)$

13. cherrilyn

okay so what should I do next

14. anonymous

You can handle it now. It is cut up in small bites that you can chew on.

15. cherrilyn

I got A = -1 and B =1 but when I find the integral my denominator = 0 :/

16. anonymous

what , just equals -ln(x) +ln(x-1) +C

17. anonymous

can be simplifed as ln [ (x-1)/(x) ] +C