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Integration via substitution problem.

  1. Aug 15, 2004 #1
    Hi, i'm currently stuck on an integration via substitution problem. I have an answer but the one given in the book of the book is different to mine. I'm wondering where exactly i've gone wrong, if i have:

    Q10: Integrate:

    x/ (x+1)^0.5 dx. Use the substitution, u^2 = x + 1.

    Heres my working:
    u^2 = x + 1.
    u = (x+1)^0.5
    2u(du/dx) = 1
    x = u^2 - 1

    So, using some substitution:

    (u^2 - 1)/u 1dx
    (u^2 - 1)/u 2u(du/dx)dx
    (u^2 - 1)2 du
    (2u^2 - 2) du

    Now integrating with respect to u:

    (2/3)u^3 - 2u

    Substituting u = (x+1)^0.5
    (2/3).(x+1)^1.5 - 2.(x+1)^0.5

    However, the actual answer given in the back of the book is:

    (2/3)(x-2).(x+1)^0.5

    Could anyone spot my mistake for me? Thanks a lot.
     
  2. jcsd
  3. Aug 15, 2004 #2
    You haven't made a mistake. (2/3)(x + 1)^1.5 - 2(x + 1)^0.5 = (x + 1)^0.5( (2/3)(x + 1)^1 - 2) = (2/3 * (x - 1)) * (x + 1)^0.5, i.e what the book wrote. Also, don't forget about the constant of integration.
     
  4. Aug 15, 2004 #3
    Ooops. Their version is just simplified. Trust me to get the part that was new to me right then forget to simplify with basic algebra >_<.
    Thanks, sorry for the stupid topic.
     
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