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Homework Help: Evaluate using any method: Essentials Of Calculus

  1. Aug 2, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\int\frac{ [(lnx)^3 - 4(lnx)^2 + 5]}{x}[/tex]dx



    2. Relevant equations



    3. The attempt at a solution

    xlnx^4 - (4/3x)lnx^3 +5x^2

    my attempt at a soultion was all wrong. The divided by x is confusing me on this one.

    The right answer is: ((lnx)^4/4) -(4/3)(lnx)^3+5lnx+C
     
    Last edited: Aug 2, 2010
  2. jcsd
  3. Aug 2, 2010 #2

    rock.freak667

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    Homework Helper

    (You forgot the 'dx' in your integral)


    but if you let u=lnx, what is du =?
     
  4. Aug 2, 2010 #3
    It would be 1/x

    What is the point of the dx after it too: is it just there for the added C?

    I got this right now and it is close:

    [tex]\int\frac{(u)^3-4(u)^2+5}{x}[/tex]dx

    [tex]\frac{(u)^4/4-(4/3)u^3+5x}{x}[/tex] + C

    I guess that 5x is suppose to be a U but I don't know why. I still have it divided by x too?
     
  5. Aug 2, 2010 #4

    rock.freak667

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    In your integral, it means what you are integrating with respect to.

    so if du/dx = 1/x, then that means that du = (1/x)dx.


    Do you see where you will have '(1/x)dx' to replace with 'du'?
     
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