Mathematics

$$\displaystyle \int_2^3\dfrac{dx}{x^2-1}$$


ANSWER

$$\dfrac{1}{2}log\dfrac{3}{2}$$


SOLUTION
$$\int _{ 2 }^{ 3 }{ \frac { dx }{ { x }^{ 2 }-1 }  } \\ \int _{ 2 }^{ 3 }{ \frac { dx }{ (x-1)(x+1) }  } \\ \frac { 1 }{ 2 } \int _{ 2 }^{ 3 }{ \frac { 1 }{ x-1 }  } -\frac { 1 }{ x+1 } \\ =\frac { 1 }{ 2 } \int _{ 2 }^{ 3 }{ \ln { (x-1) } -\ln { (x+1) }  } \\ =\frac { 1 }{ 2 } \ln { \frac { 3 }{ 2 }  } $$
Option $$D$$ is correct.
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Single Correct Medium Published on 17th 09, 2020
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