## inkyvoyd Group Title Integrate $$\Huge \frac{x}{ax^2+bx+c}$$ 2 years ago 2 years ago

1. waterineyes Group Title

2. inkyvoyd Group Title

Eh?

3. inkyvoyd Group Title

But, how exactly am I supposed to do this one?

4. waterineyes Group Title

If you put ax2 + bx + c = y then it helps or not??

5. inkyvoyd Group Title

uhh... what about the top - we just substitute using the quadratic formula in that case?

6. inkyvoyd Group Title

Sorry guys, I'm not even sure where to start with this integral. I can't find it in my book either >.<

7. eyust707 Group Title

bring everything on the bottom to the top... then integration by parts?

8. inkyvoyd Group Title

uhh - I'm not sure that will work >.<

9. eyust707 Group Title

why not...

10. inkyvoyd Group Title

All the related integrals had something to do with trig sub and inverse trig functions, but i can't find this case.

11. eyust707 Group Title

ohh

12. inkyvoyd Group Title

I know what the answer is (from an integral table), and it's logarithmic+trigonometric. I have no idea where to start though

13. inkyvoyd Group Title
14. eyust707 Group Title

ahhh that got me thinkin... let me take another look

15. eyust707 Group Title

well log came from 1/x

16. inkyvoyd Group Title

Yes.

17. eyust707 Group Title

that looks like a big u sub

18. inkyvoyd Group Title

Uh, got any ideas where to start htough?

19. eyust707 Group Title

one sec

20. inkyvoyd Group Title

kay

21. eyust707 Group Title

just by the looks w/o really thinking about it, it looks like they let the bottom = u

22. eyust707 Group Title

then factor out a 2a

23. eyust707 Group Title

1/2a *

24. eyust707 Group Title

wait wtf

25. eyust707 Group Title

lol nvm i thought the second half was the next step

26. eyust707 Group Title

thats a tricky one i need a piece of paper for that one lol

27. inkyvoyd Group Title

okay lol. Thanks for helping :P

28. eyust707 Group Title
29. eyust707 Group Title

that way is crazzyyyy tho lol

30. inkyvoyd Group Title

lol - but the answer is different from the integral table :S the result is too complicated lol. I'm using some constants for the integral that will make it even more nasty x.x

31. eyust707 Group Title

its the same just written different

32. experimentX Group Title

x = 1/2(2x + b/a) - 1/2 (b/a) make two fractions ... and use the usual approach

33. eyust707 Group Title

^^^ thats what w.a did too

34. inkyvoyd Group Title

Okay. any way to reduce it to the form seen in the integral table?

35. eyust707 Group Title

probably not

36. inkyvoyd Group Title

once i substitute my values in, it is still an intermediate result - I still have to do two more substitutions, and I'm not sure I can do the algebra without going insane.

37. experimentX Group Title

one is going to be log another ... complete squares (a+sqrt(b/4a))^2 - (b/4a-c)

38. experimentX Group Title

this is in standard form ... you should be able to evaluate this.

39. inkyvoyd Group Title

Wait, I can do it by completing the square as well?

40. experimentX Group Title

$\frac1{2a}\frac{x + b/a}{x + b/a x+c/a} - \frac1{2a}\frac{ b/a}{(x + \sqrt{b/4a})^2 - (b/4a-c/a)}$

41. inkyvoyd Group Title

oh wow. this integral - sqrt(tan x) - is a freaking pain...

42. experimentX Group Title

quite a bit ... assuming c/a > b/4a

43. eyust707 Group Title

yea just about all realistic functions are either extremely tedious or impossible to solve by hand. When it comes to practical application, we usually just have computers solve or approximate the solution.

44. inkyvoyd Group Title

Ugh, I give up. I'm tired of this integral lol. I'll look into it more tomorrow. Thanks though, @experimentX and @eyust707

45. eyust707 Group Title

thats when the mathematicians come in handy =P

46. eyust707 Group Title

yw inky.. you taking calc 2 over the summer??

47. inkyvoyd Group Title

I'm trying to finish calc 3 and linear algebra and diff equations over the summer >.<

48. eyust707 Group Title

crazyyy

49. eyust707 Group Title

that is a lot of material to learn!!

50. inkyvoyd Group Title

Yea, hopefully I can finish it.

51. eyust707 Group Title

I got faith!! where about are you in diffs?

52. inkyvoyd Group Title

Haven't even started LOL

53. eyust707 Group Title

haha I see I see

54. inkyvoyd Group Title

well, I skimmed the variables seperatble and the first order linear ODE I think

55. experimentX Group Title

It's just a substitution ... reduces to the form $\int \frac1 {x^2 + a^2}dx$ or, $\int \frac 1{x^2 - a^2}dx$ assuming first, wolf calculates 2/a arctan(x/a)

56. eyust707 Group Title

yea seps will seem very natural

57. eyust707 Group Title

linear first order with the integrating factor is tricky to understand at first... but easy to do

58. eyust707 Group Title

youll prob see frustrating word problems but dont let them scare you.. they always work out to be quite simple

59. inkyvoyd Group Title

alright - I have to learn how to integrate these nasty partial fractions first though haha :P

60. eyust707 Group Title

haha just remember, If your integrating with respect to y , all the other variables are constant!

61. eyust707 Group Title

62. eyust707 Group Title

pretend that all the other letters are just numbers and youll be golden!

63. dpaInc Group Title

didn't you see what i last posted earlier inky?

64. inkyvoyd Group Title

uhh what did you post?