Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

cutelilgirl

  • one year ago

how to integrate log | 4x^2-1| dx ?

  • This Question is Closed
  1. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    start by factoring

  2. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then break apart in to two pieces then integrate term by term

  3. Elsa213
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    erm.... integral 4x/(1+x^2) = I Let 1+x^2 = t ...........(1) --> 2x = dt/dx --> 2x dx = dt ...........(2) Now I = integral 2 [2x dx / (1+x^2) ] = integral 2 [dt / t ] since from (2) = 2 [integral dt / t ] = 2 (ln t) +c = 2 ln(1+x^2) + c We have integral 1/t dt = ln t +c Therefore I = 2 ln(1+x^2) +c where ln is log to the base e https://answers.yahoo.com/question/index?qid=20110416060345AAVswO7

  4. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @Elsa213 i am pretty sure that is some other answer to some other question

  5. Elsa213
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ik ik

  6. Elsa213
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it was just an example

  7. cutelilgirl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    log | (2x+1)(2x-1) | ??

  8. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    log a.b=loga +logb then integrate each at a time

  9. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    right

  10. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now \[\int \log(2x+1)dx+\int (2x-1)dx\]

  11. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you forgot log lol

  12. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    then you should be done because you should have the integral of the log memorized

  13. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so i did \[\int \log(2x+1)dx+\int \log(2x-1)dx\]

  14. cutelilgirl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the answer given is : x log | 4x^2-1| - 1/2 log | (2x-1)/(2x+1) | .. will i get this answer this way ?

  15. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes continue this way

  16. cutelilgirl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok thanks @xapproachesinfinity and @satellite73

  17. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you should know what is int log|x|dx

  18. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i have no idea when you integrate you will get something then using the properties of the log you can change it in to many different forms don't get married to the answer in the book

  19. cutelilgirl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    because this exercise was about the problems of integral dx / (a^2_x^2) type

  20. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i would say this integral looks nothing like that at all

  21. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    satellite you assumed that the expression will take positive values only you need the absolute value theere

  22. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i would say this integral looks nothing like that at all === is this to my reply^_^

  23. cutelilgirl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes the | 4x^2 -1 | was there

  24. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i would say \[\int \log(4x^2-1)dx\] looks nothing like \[\int \frac{dx}{a^2-x^2}\]

  25. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes i doesn't :)

  26. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it*

  27. cutelilgirl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or dx/x^2-a^2

  28. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\int \log(x)dx=x\log(x)-x\] so \[\int \log(2x+1)dx=\frac{1}{2}\left((2x+1)\log(2x-1)-(2x+1)\right)\] by a mental u sub second part is similar

  29. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @satellite73 , any reason why you took off absolute values?

  30. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    damn typo \[\int \log(2x+1)dx=\frac{1}{2}\left((2x+1)\log(2x+1)-(2x+1)\right)\]

  31. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    or if you prefer \[\frac{1}{2}(2x+1)(\log(2x+1)-1)\]

  32. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    laziness is all that and the stupid \(+ c\) got omitted as well

  33. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but you excluded the negative values?

  34. ganeshie8
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    why wolfram is giving this mess http://www.wolframalpha.com/input/?i=%5Cint+log%28abs%284x%5E2-1%29%29

  35. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wolfram is crazy hehe

  36. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i say the absolute value cannot be taken off. as we are excluding negative interval here

  37. satellite73
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    wolfram gave that mess because of the sign problem here it is neater http://www.wolframalpha.com/input/?i= \int+log%284x^2-1%29

  38. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \(\Large \rm\color{midnightblue}{\int log|(2x+1)(2x-1)|dx=\int log|2x+1|dx+\\ \int log|2x-1|dx}\)

  39. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Integration by parts should even work for the first way this expression appears

  40. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    integration by parts will be needed polynomial division partial fractions look like they are needed as well

  41. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i agree. i looks that the answer would look much simpler

  42. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x/(2x-1)(2x+1) partial fraction here

  43. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the other part is good xlog|4x^2-1|

  44. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Whenever I see something that looks like \[\int\limits_{}^{}1 \cdot \ln(f(x)) dx \] one of my first instincts it to go with the integration by parts (assuming f>0) \[=x \ln(f(x))-\int\limits_{}^{}x \frac{f'(x)}{f(x)} dx\]

  45. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so far it looks nice to me

  46. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    where did you get that @xapproachesinfinity ?

  47. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1408559618618:dw|

  48. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    from by part integration

  49. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    this now going to that expression she wrote as the answer!

  50. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I don't see where that integral comes from

  51. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i wonder if you forget f' on top |dw:1408559852906:dw|

  52. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    u=log(|4x^2-1|) ===> du=1/4x^2-1 dv=1 ====> v=x may be there is an error lol

  53. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    derivative of ln(f) is equal to f'/f

  54. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yup you are right forgot that xD

  55. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it should be what you wrote above

  56. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @cutelilgirl are you still there?

  57. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    8x^2/4x^2-1

  58. cutelilgirl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes but this seems a little beyond me :(

  59. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    have you talked about integration by parts?

  60. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that is the only way i know how to do this problem

  61. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so i assume you have had it mentioned in class

  62. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    is that a correct assumption

  63. cutelilgirl
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes

  64. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can't do partial fraction here

  65. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you know how to evaluate \[\int \ln(x) dx ]

  66. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\int\limits_{}^{} \ln(x) dx\]

  67. myininaya
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If you don't I can show you that may help you seeing this more simple integral evaluated first

  68. xapproachesinfinity
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we need another integration by part? i guess

  69. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.