Mathematics

Integrate:
$$\displaystyle\int \dfrac { v } { 1 - v } =$$


SOLUTION
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$$\begin{matrix} \Rightarrow \int { \dfrac { { 1+v-1 } }{ { \left( { 1-v } \right)  } }  }  \\ \Rightarrow \int { \dfrac { { dv } }{ { \left( { 1-v } \right)  } }  } -\int { \dfrac { { \left( { 1-v } \right) dv } }{ { \left( { 1-v } \right)  } }  }  \\ \Rightarrow -\log  \left| { 1-v } \right| -\int { dv }  \\ \Rightarrow \log { \left( { 1-v } \right) ^{ -1 } } -v+C \\ \Rightarrow \log  \dfrac { 1 }{ { \left( { 1-v } \right)  } } -v+C \\  \end{matrix}$$

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Subjective Medium Published on 17th 09, 2020
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