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Math Help - Help with indefinite integral

  1. #1
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    Help with indefinite integral

    int( -x*dx / (x+1 - sqrt(x+1) ). The book shows two answers:

    a) -x -1 -2*sqrt(x+1) + C

    b) -x -2*sqrt(x+1) + C

    By using substitution method and pattern recognition I managed to find answer (b). But I'm curious about the (a) answer.

    Thanks for any help,
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  2. #2
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    Quote Originally Posted by CalculusFan View Post
    int( -x*dx / (x+1 - sqrt(x+1) ). The book shows two answers:

    a) -x -1 -2*sqrt(x+1) + C

    b) -x -2*sqrt(x+1) + C

    By using substitution method and pattern recognition I managed to find answer (b). But I'm curious about the (a) answer.

    Thanks for any help,
    Either you have mistyped something here, or they are the same thing.

    If C is an arbitary conatant then so is K = C-1 so look at (a):

    <br />
-x -1 -2\sqrt{x+1} + C=-x -2\sqrt{x+1} + (C-1)=-x -2\sqrt{x+1} + K<br />

    RonL
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  3. #3
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    Maybe you are wright, CaptainBlak; but what intrigued me was Maple's answer: it also shows -x -1 -2*sqrt(x+1); and Maple is known for being carefree with constants.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by CalculusFan View Post
    Maybe you are wright, CaptainBlak; but what intrigued me was Maple's answer: it also shows -x -1 -2*sqrt(x+1); and Maple is known for being carefree with constants.
    The Integrator also gives that answer
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