## inkyvoyd Group Title Integrate $$\frac{-\frac{1}{\sqrt{2}v}}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}$$ 2 years ago 2 years ago

1. inkyvoyd Group Title

@nbouscal will know what I am talking about, or maybe @Limitless

2. inkyvoyd Group Title

Wait, correction.

3. inkyvoyd Group Title

$$\frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}$$

4. inkyvoyd Group Title

Am I supposed to complete the square?

5. inkyvoyd Group Title

@dpaInc , pwease help me!

6. dpaInc Group Title

can't see it so i'm gonna copy it... and make it huge... $\huge \frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}$

7. inkyvoyd Group Title

@dpaInc , how do you copy it like that?

8. dpaInc Group Title

right click-->show math as-->tex commands

9. dpaInc Group Title

$\huge \int\frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}dv$

10. inkyvoyd Group Title

Alright, now solve NAO!

11. inkyvoyd Group Title

xD

12. inkyvoyd Group Title

btw, this is the equation I got after trying 3 substitutions and seperating the fraction.

13. dpaInc Group Title

$\large \int\frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}dv$ $\large \frac{-1}{\sqrt2}\int\frac{v}{v^2+\sqrt{2}v+1}dv+\frac{1}{\sqrt2}\int \frac{v}{v^2-\sqrt{2}v+1}dv$ maybe i should just draw...

14. inkyvoyd Group Title

lolol

15. inkyvoyd Group Title

@dpaInc , now do I complete the square?

16. dpaInc Group Title

yeah... that's what i was about to do... but i think there is a formula... hang on....

17. dpaInc Group Title

18. dpaInc Group Title

i mean #16...l

19. inkyvoyd Group Title

$$\huge \frac{-1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v-\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv$$

20. inkyvoyd Group Title

But isn't using tables cheating?

21. dpaInc Group Title

no... of course not...

22. inkyvoyd Group Title

But... I don't know where the tables come from... >.<

23. dpaInc Group Title

it's like using all the different tires for your car... you're not going to make/invent your own tires are you? oh wait.. do you drive yet?

24. inkyvoyd Group Title

No lol. I'M GOING TO BUILD MY CAR FROM SCRATCH MUAHAHAHA

25. dpaInc Group Title

i don't think it's cheating... it's a good shortcut to cut through all that stuff..

26. inkyvoyd Group Title

Okay... @dpaInc , without showing me the math, can you tell me what to do after I have completed the square?

27. dpaInc Group Title

and as for me, i haven't really started using the integral tables until i saw everyon virtually used them here on OS.... i actually went through proving stuff because I don't use/memorize the tables...

28. inkyvoyd Group Title

@dpaInc , my problem is that I'm not sure how to get the results shown in the tables.

29. dpaInc Group Title

let me complete the square on the first integral... i haven't done it for a while and i guess i need the practice...

30. inkyvoyd Group Title

I already did in my last tex post :)

31. inkyvoyd Group Title

\huge \frac{-1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v-\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv

32. dpaInc Group Title

oh... i see you did it already....

33. inkyvoyd Group Title

xD

34. nitz Group Title

you are solving the problem in a wrong way

35. inkyvoyd Group Title

@nitz , what am I doing wrong?

36. nitz Group Title

see firstly make numerator as the derivative of denominator

37. inkyvoyd Group Title

Can you show me?

38. nitz Group Title

39. inkyvoyd Group Title

?

40. nitz Group Title

in it, firstly multiply the numerator with 2 and add and subtract $\sqrt{ 2}$ in it

41. inkyvoyd Group Title

You mean at the very start of the problem?

42. nitz Group Title

ya

43. inkyvoyd Group Title

but but but

44. inkyvoyd Group Title

$$\huge \frac{-1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v-\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv$$ we already got to here >.<

45. nitz Group Title

you cant solve it further in this case

46. inkyvoyd Group Title
47. nitz Group Title

these are direct problems

48. nitz Group Title

these are direct solutions

49. nitz Group Title

you can apply direct formula

50. dpaInc Group Title

i think it works.... |dw:1340004704215:dw|

51. inkyvoyd Group Title

Uh, I can't use u in substiution LOL. I already used it...

52. nbouscal Group Title

Okay, I'm late to this party, but you can just complete the square and then do a substitution. This is just like the case that we reach in the integration of sqrt(tan x) that we have already done, inky.

53. Limitless Group Title

Next OS question: What made this integral appealing? I will medal the person with the best response.

54. nbouscal Group Title

This actually looks very similar to the integral of sqrt(tan x), if I had to guess I would say it is an intermediate step in a similar integration.

55. inkyvoyd Group Title

@nbouscal , that was my integration of the square root of tan x...

56. Limitless Group Title

nbouscal: Integral Detective

57. inkyvoyd Group Title

Maybe I should show what work i did before...

58. nbouscal Group Title

I didn't actually go back and look at that integral, you're probably right on. The next step is indeed to complete the square, then do another substitution.

59. nbouscal Group Title

Oh hey just look here: http://openstudy.com/study#/updates/4fb3c611e4b0556534298c6b