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Integrate x/(x+1)^1/2

  1. Feb 1, 2009 #1
    Hi,

    I am trying to work a problem that seems to have me stumped.

    ∫x/√(x+1) dx


    I have tried to look at it as a right triangle with:
    hypotenouse = √(x+1)
    sideA = 1
    sideB = √x

    So I have:
    cot^2 ∅=x, dx=-2cot∅csc^2 ∅ d∅
    csc∅=√(x+1)

    Working through the problem I have
    -2∫(cot^2 ∅/csc∅) * cot∅csc^2 ∅ d∅
    -2∫cot^3 ∅ * csc∅ d∅
    -2∫(cos^3 ∅/sin^3 ∅) * (1/sin∅) d∅
    -2∫cos^3 ∅/sin^4 ∅ d∅

    Trying to solve it from here using more identities just keeps getting messier and I don't seem to be making any progress.

    So, my main question is "am I on the right track?" or "is there an easier way that I am overlooking?"

    Thank You,

    James
     
  2. jcsd
  3. Feb 1, 2009 #2

    Dick

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    Science Advisor
    Homework Helper

    There's a way easier route. Try the substitution u=x+1. x=u-1. The triangles aren't helping at all.
     
  4. Feb 1, 2009 #3
  5. Feb 1, 2009 #4
    I am not sure how I made it that difficult except that I have been staring at this way too long today. Dicks method was much easier and greatly appreciated. Thanks to both of you.

    James
     
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