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Asylum15

  • 3 years ago

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  1. Asylum15
    • 3 years ago
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    \[\int\limits \frac{ lnx }{ x }\]

  2. Asylum15
    • 3 years ago
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    Whos feelin brave? :D

  3. TuringTest
    • 3 years ago
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    I'm thinking by parts...

  4. surdawi
    • 3 years ago
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    u du

  5. Siddharth18
    • 3 years ago
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    do it by substitution, let lnx= u

  6. TuringTest
    • 3 years ago
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    haha, oh yeah, I overthought it :P

  7. Asylum15
    • 3 years ago
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    Can U be lnx ? It's above the line

  8. TuringTest
    • 3 years ago
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    so?

  9. surdawi
    • 3 years ago
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    |dw:1353166961045:dw|

  10. Siddharth18
    • 3 years ago
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    |dw:1353035523772:dw|

  11. waterineyes
    • 3 years ago
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    Put ln(x) = u So: \(\frac{1}{x} \cdot dx =du\)

  12. Asylum15
    • 3 years ago
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    Thank you guys

  13. waterineyes
    • 3 years ago
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    Just try and if you face any problem, then do ask us...

  14. Asylum15
    • 3 years ago
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    Wait, can you expand on that for me? I have \[dx = \frac{ du }{ 1/x }\]

  15. waterineyes
    • 3 years ago
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    Are you converting a simple solution to hard one??

  16. Asylum15
    • 3 years ago
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    Looks like it xD

  17. waterineyes
    • 3 years ago
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    |dw:1353167337486:dw|

  18. waterineyes
    • 3 years ago
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    Sorry, my handwriting is not too good..

  19. Asylum15
    • 3 years ago
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    Is this a direct manipulation or a substitution?

  20. waterineyes
    • 3 years ago
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    Is this not Substitution ?? We are substituting u in place of x..

  21. Asylum15
    • 3 years ago
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    Ah, ok, so lnx. Differentiation of ln = 1 over So 1/x right?

  22. waterineyes
    • 3 years ago
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    Yes..

  23. waterineyes
    • 3 years ago
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    \[\frac{d}{dx}\ln(x) = \frac{1}{x}\]

  24. Asylum15
    • 3 years ago
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    So, let me just clarify. lnx / x = 1/x?

  25. Asylum15
    • 3 years ago
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    Where does the x under the line go?

  26. waterineyes
    • 3 years ago
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    See : \[\ln(x) = u\] Right ??

  27. Asylum15
    • 3 years ago
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    Yes

  28. waterineyes
    • 3 years ago
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    Now take derivative both the sides and tell what did you get??

  29. Asylum15
    • 3 years ago
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    Next, i've been taught to do du/dx

  30. Asylum15
    • 3 years ago
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    1/x . dx

  31. waterineyes
    • 3 years ago
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    Write them properly.. with LHS and RHS..

  32. Asylum15
    • 3 years ago
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    Little lost here, sorry :(

  33. Asylum15
    • 3 years ago
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    1/x . dx = du

  34. waterineyes
    • 3 years ago
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    Do you know how it came??

  35. Asylum15
    • 3 years ago
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    Yes i get this.

  36. Asylum15
    • 3 years ago
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    What is the next step?

  37. waterineyes
    • 3 years ago
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    Just use this to substitute these values in your question..

  38. Asylum15
    • 3 years ago
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    I think the way i've been taught is conflicting... I usually write dx = du / 1/x

  39. Asylum15
    • 3 years ago
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    If substituting

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