Mathematics

# $\displaystyle \int { \frac { 1 }{ { 9x }^{ 2 }-1 } dx }$

##### SOLUTION
$\displaystyle \int \dfrac{1}{9x^2-1}dx$
$\implies \displaystyle\int \dfrac{1}{(3x)^2-(1)^2}dx$

$\implies \displaystyle \int \dfrac{1}{(3x-1)(3x+1)}dx$

$\implies \dfrac{1}{2}(\displaystyle \int \dfrac{1}{(3x-1)}-\dfrac{1}{(3x+1)}dx)$

$\implies \dfrac{1}{2} log\dfrac{(3x-1)}{(3x+1)}+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

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$\displaystyle \int\frac{dx}{(\sin^{-1} x)^{3}\sqrt{1-x^{2}}}=$
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• C. $\displaystyle \frac{1}{4(\sin^{-1} x)^{2}}+c$
• D. $\displaystyle \frac{-1}{2(\sin^{-1} x)^{2}}+c$

1 Verified Answer | Published on 17th 09, 2020

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