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Math Help - integral

  1. #1
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    integral

    intergral x((2x)/(x^2+1))dx
    Somebody mentioned a sub u= x^2+1 so it is then ln (x^2+1) but what about the x in front of the problem
    Last edited by Bust2000; March 4th 2008 at 08:51 AM.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Bust2000 View Post
    X ((2x)/(X^2+1))dx
    Somebody mentioned a sub u= x^2+1 so it is then ln (x^2+1) but what about the x in front of the problem
    do you know hot to do the substitution?

    if u = x^2 + 1 then du = 2x \, dx

    get it already?
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  3. #3
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    Hello, Bust2000

    X ((2x)/(X^2+1))dx
    Check the original problem again . . .

    Is that really an x in front?
    . . Could it be somebody's multiplication-sign?

    Why wasn't the problem presented as: . \int \frac{2x^2}{x^2+1}\,dx

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  4. #4
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    Yes really an x in front

    yes there really is an x in front not a multiplication sign
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  5. #5
    Super Member wingless's Avatar
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    If it's really \int \frac{2x^2}{x^2 + 1}~dx,

    2\int \frac{x^2}{x^2 + 1}~dx

    \frac{x^2}{x^2 + 1} = 1-\frac{1}{x^2 + 1}

    So it becomes, 2 \left ( \int 1~dx - \int \frac{1}{x^2+1}~dx \right )

    2 \left ( x - \text{Arctan}x \right )

    2x - 2\text{Arctan}x
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