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Math Help - [SOLVED] Integration is not my bag

  1. #1
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    [SOLVED] Integration is not my bag

    Can someone please walk me through how to integrate

    int. of ((3x^2)-7x-2)/ ((x^3) -x)

    I appreciate everyones help on here
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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     <br />
\int\frac{3x^2-7x-2}{x^3-x}\,dx=\int\frac{(4x^2+2x^2-3x^2)-(4x+3x)-2}{x(x+1)(x-1)}\,dx

    Then

    \int\frac{(4x^2-4x)+(2x^2-2)-(3x^2+3x)}{x(x+1)(x-1)}\,dx

    Now we have

    \int\frac{4x(x-1)+2(x+1)(x-1)-3x(x+1)}{x(x+1)(x-1)}\,dx

    which is equal to

    \int\frac4{x+1}\,dx+\int\frac2x\,dx-\int\frac3{x-1}\,dx

    Finally

    \int\frac{3x^2-7x-2}{x^3-x}\,dx=4\ln|x+1|+2\ln|x|-3\ln|x-1|+k<br />

    --

    If it just LaTeX could allow bigger images and more characters (only supports 400), I could've aligned this.
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