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Math Help - Integration

  1. #1
    Member roshanhero's Avatar
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    Integration

    \int \frac{x(1+x^2)}{1+x^4)}
    I tried to do it by substitution but reached nowhere
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  2. #2
    Super Member Anonymous1's Avatar
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    Hint:
    \int \frac{1}{1+x^2} = tan^{-1}(x)

    oops..
    Last edited by Anonymous1; March 31st 2010 at 11:25 PM.
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  3. #3
    Super Member Anonymous1's Avatar
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    Another hint:

    \int \frac{x+x^3}{1+x^4} = \int \frac{x}{1+x^4} + \int \frac{x^3}{1+x^4}
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  4. #4
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    Quote Originally Posted by Anonymous1 View Post
    Hint:
    \int \frac{1}{1+x^4} = tan^{-1}(x^2)
    This is NOT correct.

    But we can observe that:

    \frac{d}{dx} \tan^{-1}(x^2) = \frac{2x}{1+(x^2)^2}

    However, if you didn't recognize this, you'd have to do a bit more work with partial fractions, etc.
    Last edited by drumist; March 31st 2010 at 11:00 PM.
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  5. #5
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    Quote Originally Posted by roshanhero View Post
    \int \frac{x(1+x^2)}{1+x^4)}
    I tried to do it by substitution but reached nowhere
    Use the substitution u = x^2.

    If you need more help, please show your work and say where you get stuck.
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