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Math Help - Integral

  1. #1
    Member Jason Bourne's Avatar
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    Integral

    \int \frac{1+v}{1-2v-v^2} dv

    I know this equals \frac{-1}{2}log(1-2v-v^2) + C but I don't know how to get to it.
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  2. #2
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    Sub u = 1 - 2v - v^2 and see what you get.
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  3. #3
    o_O
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    {\color{red}u = 1 - 2v - v^2} \ \ \Rightarrow \ \ du = (-2 - 2v) \ dv \Leftrightarrow {\color{blue}-\frac{du}{2} = (v+ 1) \ dv}

    So: \int \frac{{\color{blue} v+1}}{{\color{red}1-2v-v^2}} {\color{blue} \ dv} \ = \cdots
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  4. #4
    Member Jason Bourne's Avatar
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    thanks, I didn't realise it was that simple.
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