## cherrilyn 5 years ago evaluate the integral

1. cherrilyn

$\int\limits_{?}^{?}100xdx/(x-3)(x ^{2}+1)^{2}$ I know I change it to A/x-1 + B(x-1)^2+C(x-1)^3 then multiply it by (x-1)^3 then what

2. anonymous

are you sure?

3. cherrilyn

oops I mean A/x-3 + Bx+C/x^2+1 + Dx+E/(x^2+1)^2

4. anonymous

lol

5. anonymous

alright, good , now start taking small values for x ^_^ to find A, B, C and D

6. anonymous

wait, first you have to multiply the denominator on all parts

7. anonymous

Take x=3. You will find A directly.

8. anonymous

A=3

9. anonymous

so, you'll get :$100x = A(x+1)^2 + Bx + C(x-3)(x^2+1) + Dx + E (x-3)$

10. cherrilyn

ok A=3 :)

11. cherrilyn

wait no

12. anonymous

now you can take values for x to find all the alphabets ^_^

13. anonymous

hmm, what?

14. cherrilyn

when you distribute in..for example.. Bx+C(x-3)(x^2+1) ... do you distribute the two things in the parenthesis to the Bx AND the C? or just the C

15. cherrilyn

and Distribute (x-3) to the Dx AND the E?

16. anonymous

hmm, I think it's the whole thing

17. anonymous

yes yes, I'm sure

18. cherrilyn

okay so A is indeed 3

19. anonymous

yes it is ^_^

20. anonymous

The better way is to open all brackets, and add like terms together.

21. anonymous

now take other values for x, such as -1 1 2 -2 ~

22. anonymous

B=0

23. anonymous

Oh wait!!

24. cherrilyn

blaah do I have to test all of those numbers? lol its kiind of hard to predict the right values just by looking at it

25. anonymous

yes it's a must, you need to get all the values, A, B,C,D,and E

26. cherrilyn

I mean the numbers -1, 1, 2, and -2

27. anonymous

yes , you must lol, what other way is there to solve it?

28. anonymous

you must check with all values my dear :)

29. anonymous

B=-3

30. anonymous

C=9

31. anonymous

you checked the values? anwar? or shall I check after you lol

32. anonymous

D=18

33. cherrilyn

Okay If I plug in A=3 and x=-1..... I get -100=12+2B-2C+4D-4E. now what? Or am I doing this wrong

34. anonymous

no you're write, so now you have equation 1, you can use it later to either subtract or add from another equation ^_^

35. anonymous

right*

36. anonymous

alright I gtg, I'll be back later, bye ^_^

37. cherrilyn

okay thankss! Ttyl :)

38. anonymous

anwar will continue, most welcome :)

39. anonymous

I got all of them. Hopefully right!

40. anonymous

A=3, B=-3, C=9, D=24, E=-8

41. anonymous

Bye starica!!

42. cherrilyn

thanks anwar!

43. anonymous

You're welcome!! You may want to check them.

44. anonymous

OMG, Sorry there was a mistake.

45. anonymous

It should be: A=3, B=-3, C=-9, D=-30, E=10. Sorry for the confusion.

46. cherrilyn

what values for x did you use?

47. anonymous

Well.. I opened all the parenthesis, and add like terms together, and then solved the equations.

48. anonymous

For example if you have x^2(A+B)+x(C+2B)=5x^2+x, that means: A+BC=5 and C+2B=1.. I used this idea.