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Math Help - [SOLVED] integration

  1. #1
    Member ronaldo_07's Avatar
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    [SOLVED] integration

    \int \frac{-4x}{4x^4+4x^2+1}

    \int \frac{-4x}{(2x^2+1)(2x^2+1)}

    What would my next steps be to complete this integral?
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  2. #2
    MHF Contributor red_dog's Avatar
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    Use the substitution 2x^2+1=t\Rightarrow 4xdx=dt
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  3. #3
    Member ronaldo_07's Avatar
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    \int\frac{-4x}{t^2}*\frac{dt}{4x}

    \int\frac{1}{(2x^2+1)(2x^2+1)}

    is this correct?
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  4. #4
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    And, if a picture helps...



    Straight continuous lines differentiate/integrate with respect to x, the straight dashed line with respect to the dashed balloon expression - as though it were a variable like u.

    Don't integrate - balloontegrate! Balloon Calculus: worked examples from past papers
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  5. #5
    Member ronaldo_07's Avatar
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    As my answer I got y=\frac{1}{2x^2+1}+C
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  6. #6
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    Yep
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  7. #7
    Member ronaldo_07's Avatar
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    thanks
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  8. #8
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    Quote Originally Posted by ronaldo_07 View Post
    As my answer I got y=\frac{1}{2x^2+1}+C
    You can always differentiate it and see if you get back the integrand.
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  9. #9
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    Yes - and of course the differentiation is the same picture (completed) but read downwards instead of up.





    Don't integrate - balloontegrate! http://www.ballooncalculus.org/examples.png
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