∫19x^2 1dx #160; ∫1(3x)^2 (1)^2dx #160; ∫1(3x 1)(3x+1)dx 12(∫1(3x 1) 1(3x+1)dx) 12 log(3x 1)(3x+1)+C ...

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Factorization Method Form to Remove Indeterminate Form

∫ 1 / 9x 2 -1...

Question

$\int \frac{1}{{9 x}^{2} - 1} d x$

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Solution

$\int \frac{1}{9 x^{2} - 1} d x$
$⟹ \int \frac{1}{(3 x)^{2} - (1)^{2}} d x$

$⟹ \int \frac{1}{(3 x - 1) (3 x + 1)} d x$

$⟹ \frac{1}{2} (\int \frac{1}{(3 x - 1)} - \frac{1}{(3 x + 1)} d x)$

$⟹ \frac{1}{2} l o g \frac{(3 x - 1)}{(3 x + 1)} + C$

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Similar questions

\int \frac{1}{9 x^{2} - 1} d x

lim x \to \infty \frac{\sqrt{1 + 25 x^{2}} + \sqrt{9 x^{2} - 1}}{\sqrt{1 + 25 x^{2}} - \sqrt{9 x^{2} - 1}} =

{9 x}^{2} + \frac{1}{{9 x}^{2}} - 2 = 0

3 x + \frac{1}{3 x} = 3

9 x^{2} + \frac{1}{9 x^{2}}

9 x^{2} + \frac{1}{9 x^{2}}

(3 x + \frac{1}{3 x}) = \frac{8}{3}

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