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Integration methods

  1. Jul 12, 2009 #1
    1. The problem statement, all variables and given/known data

    I(xlnx/(x^2-1)^(1/2),x)
    x=secT ; dx=secTtanTdT
    I(secTln(secT)secTtanTdT/tanT,T)
    I(sec^2Tln(secT),T)
    u=ln(secT) du= secTtanTdT/secT = tanTdT
    dv=sec^2Tdt v=tanT
    tanTln(secT)- I(tan^2T,T)
    tanTln(secT)-I(sec^2-1,T)
    tanTln(secT)-tanT+T+C
    T=sec^-1x
    secT=x
    tanT= (x^2-1)^(1/2)
    tanTln(secT)-tanT-T= (x^2-1)^(1/2)lnx-(x^2-1)^(1/2)+sec^-1x+C

    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 12, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi nameVoid! :smile:

    (have an integral: ∫ and a square-root: √ and try using the X2 tag just above the Reply box :wink:)

    Yes, that looks correct, but you could have missed out a lot in the middle if you'd noticed that x/√(x2 - 1) is an exact integral, so you can integrate by parts immediately. :wink:
     
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