Mathematics

# Find :$\displaystyle\int {\dfrac{2}{(1-x)(1+x^2)}dx}$

##### SOLUTION

We have,

$I=\displaystyle\int{\dfrac{2}{\left( 1-x \right)\left( 1+{{x}^{2}} \right)}dx}$

$I=\displaystyle\int{\left( \dfrac{1}{1-x}+\dfrac{x+1}{1+{{x}^{2}}} \right)dx}$

$I=-\displaystyle\int{\left( \dfrac{1}{x-1} \right)dx+\dfrac{1}{2}}\displaystyle\int{\left( \dfrac{2x}{1+{{x}^{2}}} \right)dx+\displaystyle\int{\left( \dfrac{1}{1+{{x}^{2}}} \right)dx}}$

$I=-\ln \left( x-1 \right)+\dfrac{1}{2}\ln \left( {{x}^{2}}+1 \right)+{{\tan }^{-1}}x+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

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