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Math Help - Integration By Partial Fractions - Urgent Help Please

  1. #1
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    Integration By Partial Fractions - Urgent Help Please

    integral(x/(x^2+4x+13),x,0,1)

    I broke the bottom up to (x+2)^2 + 9, but now I"m stuck. any help would be very appreciated.

    Thanks,
    s3n4te

    edit: i think i should now use inverse trig substitution.
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  2. #2
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    Hi

    2x+4)}{x^2+4x+13} - \frac{2}{(x+2)^2+9}" alt="\frac{x}{x^2+4x+13} = \frac{\frac{1}{2}\2x+4)}{x^2+4x+13} - \frac{2}{(x+2)^2+9}" />

    The first part is integrable in \frac{1}{2}\:ln|x^2+4x+13|

    The second part is integrable in Arctan after setting x+2=3t
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  3. #3
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    How do you know how to split that up like that?
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  4. #4
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    Quote Originally Posted by s3n4te View Post
    How do you know how to split that up like that?
    By experience

    You make \frac{u'}{u} appear eventually using a multiplicative constant - here \frac{1}{2}

    The other part is then integrable with Arctan (this is true because the denominator has no real roots)
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