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Math Help - Integral Help!

  1. #1
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    Integral Help!

    I have this problem (forgive me, i haven't gotten the math controls down yet):

    Integral 7x/(1+3x^2)^2 dx

    here's what I've done so far:
    A/(1+3x^2) + B/(1+3x^2)^2
    = A(1+3x^2)+B(1+3x^2)/ (1+3x^2)^2
    = A(1+3x^2)+B

    I'm stuck right there. I can't figure out how to solve for A and B. Any help is greatly appreciated.

    Cheers
    Last edited by jschlarb; May 19th 2008 at 11:10 AM. Reason: Forgot a square
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  2. #2
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    No need for partial fractions.

    7\int\frac{x}{1+3x^{2}}dx

    Let u=1+3x^{2}, \;\ du=6xdx, \;\ \frac{1}{6}du=xdx

    \frac{7}{6}\int\frac{1}{u}du

    \frac{7}{6}ln(u)

    \frac{7}{6}ln(3x^{2}+1)
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  3. #3
    Super Member flyingsquirrel's Avatar
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    Hello

    A/(1+3x^2) + B/(1+3x^2)^2
    The partial fractions decomposition of \frac{7x}{1+3x^2} is \frac{\alpha}{x-a}+\frac{\beta}{x-b} where a and b are the two complex roots of 1+3x^2
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  4. #4
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    Quote Originally Posted by galactus View Post
    No need for partial fractions.

    7\int\frac{x}{1+3x^{2}}dx

    Let u=1+3x^{2}, \;\ du=6xdx, \;\ \frac{1}{6}du=xdx

    \frac{7}{6}\int\frac{1}{u}du

    \frac{7}{6}ln(u)

    \frac{7}{6}ln(3x^{2}+1)

    The denominator is supposed to be squared

    7\int\frac{x}{{(1+3x^{2})}^2}dx

    Does that change anything?
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  5. #5
    Moo
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    Hello,

    Quote Originally Posted by jschlarb View Post
    The denominator is supposed to be squared

    7\int\frac{x}{{(1+3x^{2})}^2}dx

    Does that change anything?
    You can directly calculate the integral, by substituting u=1+3x^2
    --> du=6x dx \implies dx=\frac{du}{6x}

    7 \int \frac{x}{(1+3x^2)^2} dx=7 \int \frac{x}{u^2} \cdot \frac{1}{6x} dx=\frac 76 \int \frac{du}{u^2}=-\frac 76 \cdot \frac 1u

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  6. #6
    Moo
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    If you want to calculate it by partial fractions :

    You're looking for A, B, C and D such that :

    \frac{x}{(1+3x^2)^2}=\frac{Ax+B}{1+3x^2}+\frac{Cx+  D}{(1+3x^2)^2}, which is, I think you agree with it, quite complicated


    You can look at this link : Quick Guide Partial Fractions
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