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
Questions 203525
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