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anilorap

i want to confirm the answer of... integrate lnx/x dx

  • 2 years ago
  • 2 years ago

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  1. anilorap
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    my answer is ln lxl +c

    • 2 years ago
  2. myininaya
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    let u=lnx du=dx/x \[\int\limits_{}^{}u du=\frac{u^2}{2}+C=\frac{(lnx)^2}{2}+C\] we can even check this: \[(\frac{(lnx)^2}{2}+C)'=2*\frac{lnx}{2}*\frac{1}{x}+0=\frac{lnx}{x}\]

    • 2 years ago
  3. myininaya
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    do you got it?

    • 2 years ago
  4. anilorap
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    yes

    • 2 years ago
  5. myininaya
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    k :)

    • 2 years ago
  6. anilorap
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    q. how do i know what to choose?

    • 2 years ago
  7. myininaya
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    i was looking for \[\int\limits_{}^{}f(x)*f'(x)dx\]

    • 2 years ago
  8. myininaya
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    sometimes its not always that easy though

    • 2 years ago
  9. myininaya
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    someone said it is like an art and i agree

    • 2 years ago
  10. anilorap
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    jajaj..ok

    • 2 years ago
  11. myininaya
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    it is not always easy to know what substititon to make but since it was in the form of above it was easy let u=f(x) du=f'(x) dx

    • 2 years ago
  12. myininaya
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    \[\int\limits_{}^{}\frac{lnx}{x}dx=\int\limits_{}^{}lnx*\frac{1}{x} dx\]

    • 2 years ago
  13. myininaya
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    so it was easy for me to notice pretty fast that (lnx)'=1/x so thats why i let u=lnx

    • 2 years ago
  14. anilorap
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    ok..perfect

    • 2 years ago
  15. anilorap
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    so how can i integrate tanx dx..... even though i know thats it is equal to -lnlcosxl+c

    • 2 years ago
  16. myininaya
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    \[\int\limits_{}^{}\frac{sinx}{cosx} dx\] right?

    • 2 years ago
  17. myininaya
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    tanx=sinx/cosx agree?

    • 2 years ago
  18. anilorap
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    ohhhhhhhh... ok

    • 2 years ago
  19. anilorap
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    yes

    • 2 years ago
  20. anilorap
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    so that du/u

    • 2 years ago
  21. myininaya
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    now what do you think the substitution will be?

    • 2 years ago
  22. anilorap
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    with the negative sign of the sin

    • 2 years ago
  23. anilorap
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    u=cos

    • 2 years ago
  24. anilorap
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    du=sin x

    • 2 years ago
  25. anilorap
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    sorry du=-sinx

    • 2 years ago
  26. myininaya
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    du=-sinx dx (i like not to forget about this dx part)

    • 2 years ago
  27. anilorap
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    oh yea

    • 2 years ago
  28. myininaya
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    so show me what that gives us don't integrate yet

    • 2 years ago
  29. anilorap
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    then u have integral of du/u

    • 2 years ago
  30. myininaya
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    negative or positive?

    • 2 years ago
  31. anilorap
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    - integral of du/u

    • 2 years ago
  32. myininaya
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    yes and now integrate

    • 2 years ago
  33. anilorap
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    so my result will be -ln/u/+c

    • 2 years ago
  34. anilorap
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    -ln/cosx/+c

    • 2 years ago
  35. myininaya
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    yes :)

    • 2 years ago
  36. anilorap
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    yeaaa thank uuuu

    • 2 years ago
  37. myininaya
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    np

    • 2 years ago
  38. myininaya
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    so whats this \[\int\limits_{}^{}-tanx dx\] equal to?

    • 2 years ago
  39. anilorap
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    ln/cosx/+c

    • 2 years ago
  40. anilorap
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    becuase the negative sign will change to postive once u take the derivative of cosx

    • 2 years ago
  41. anilorap
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    why u pic u =sinx?

    • 2 years ago
  42. myininaya
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    accident

    • 2 years ago
  43. myininaya
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    u=cosx du=-sinx dx

    • 2 years ago
  44. anilorap
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    :)

    • 2 years ago
  45. anilorap
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    good....:

    • 2 years ago
  46. myininaya
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    you want to try one i made up? its not hard

    • 2 years ago
  47. anilorap
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    ok

    • 2 years ago
  48. myininaya
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    \[\int\limits_{}^{}\frac{x+1}{x^2+2x}dx\]

    • 2 years ago
  49. anilorap
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    ok.. let me try

    • 2 years ago
  50. anilorap
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    u=x^2 + 2x du=2x+2 dx =2(x+1) dx so, 1/2du=x+1 dx

    • 2 years ago
  51. myininaya
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    very good so far

    • 2 years ago
  52. anilorap
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    1/2 integral of du/u =1/2 lnlul+c =1/2 ln/x^2+2xl+c

    • 2 years ago
  53. myininaya
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    :)

    • 2 years ago
  54. anilorap
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    yeaaaaaaaaaaaaa

    • 2 years ago
  55. anilorap
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    i love this stuff

    • 2 years ago
  56. myininaya
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    lol it is nice

    • 2 years ago
  57. myininaya
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    \[\int\limits_{}^{}\frac{f'(x)}{f(x)}dx\] so when we have this what will out answer be in the form of?

    • 2 years ago
  58. anilorap
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    f(x)*f'(x)

    • 2 years ago
  59. myininaya
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    look at the one you just did didn't we have f'/f dx?

    • 2 years ago
  60. anilorap
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    ohh... sorry.. yes yes

    • 2 years ago
  61. myininaya
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    =ln|f(x)|+C

    • 2 years ago
  62. anilorap
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    yes

    • 2 years ago
  63. myininaya
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    \[\int\limits_{}^{}[f(x)]^n*f'(x)dx\] \[n \neq -1\] what about this? what will our answer be?

    • 2 years ago
  64. myininaya
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    i will give you a hint let u=f(x) so du=f'(x) dx

    • 2 years ago
  65. anilorap
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    jjajjjaj... nice hint

    • 2 years ago
  66. myininaya
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    where are you from? you say jajaja alot lol

    • 2 years ago
  67. anilorap
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    dominican republic

    • 2 years ago
  68. anilorap
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    i am just laughing

    • 2 years ago
  69. myininaya
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    jajaaja= laughing?

    • 2 years ago
  70. anilorap
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    yess... how can i laugh??

    • 2 years ago
  71. myininaya
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    its fine the way you type your laughter no worries i like it

    • 2 years ago
  72. anilorap
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    lol

    • 2 years ago
  73. myininaya
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    so this all makes a little more sense?

    • 2 years ago
  74. myininaya
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    the integral stuff?

    • 2 years ago
  75. anilorap
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    why?

    • 2 years ago
  76. myininaya
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    im asking do you get the integral stuff better?

    • 2 years ago
  77. anilorap
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    ohhhhhh,, yess

    • 2 years ago
  78. myininaya
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    good :) im fixing to go to sleep goodnight

    • 2 years ago
  79. anilorap
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    for me is mornig.. but good nigth,,,

    • 2 years ago
  80. myininaya
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    good morning* i didn't sleep all night lol

    • 2 years ago
  81. anilorap
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    jajajajaaja

    • 2 years ago
  82. anilorap
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    ayayay.. no good

    • 2 years ago
  83. anilorap
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    thank u very much...

    • 2 years ago
  84. myininaya
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    np if you want to try another this is a good one \[\int\limits_{}^{}x*\sqrt{x+1} dx\] the answer is given above in one of the other threads if you want to check yourself

    • 2 years ago
  85. myininaya
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    later

    • 2 years ago
  86. anilorap
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    ok,, thanks

    • 2 years ago
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