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
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