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Integral substitiotion

  1. Oct 19, 2006 #1
    evaluate the indefinite integral sqrt(2x+1)dx

    I let u^2 = 2x+1

    then

    indefinite integral u^2du

    1/3u^3 + C

    1/3(sqrt(2x+1))^3 + C is my finals answer

    can this also be written like this 1/3(2x+1)^3/2 + C?


    Thanks
     
  2. jcsd
  3. Oct 19, 2006 #2
    yes you are correct
     
  4. Oct 19, 2006 #3

    quasar987

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    Your answer is right, but I have no idea what you just did. Would you mind explaining it to me?
     
  5. Oct 19, 2006 #4
    sure,

    I skipped a few steps in my previous post.

    evaluate the indefinite integral sqrt(2x+1)dx

    u = sqrt(2x+1)

    du = dx/sqrt(2x+1)

    sqrt(2x+1)du = dx

    or

    udu = dx

    rewriting the integral

    indefinite integral u x udu

    = indefinite integral u^2du

    then just take antiderivative of u^2 and substitute sqrt(2x+1) back into it
     
  6. Oct 19, 2006 #5

    quasar987

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    oooh, I see now, thx!
     
  7. Oct 20, 2006 #6

    HallsofIvy

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    Probably Quasar987 was used the substitution u= 2x+1 which gives the same answer.
     
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