Question

Evaluate: integrate dx/4x^2-9
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Answer 1

hope it's USEFUL!!!!!!!!

Answer 2

SOLUTION

TO INTEGRATE

$\displaystyle \int\limits_{}^{} \, \frac{dx}{4 {x}^{2} - 9}$

FORMULA TO BE IMPLEMENTED

We are aware of the formula on integration that

$\displaystyle \int\limits_{}^{} \, \frac{dx}{ {x}^{2} - {a}^{2} } = \frac{1}{2a} \log \bigg| \frac{x - a}{x + a} \bigg| + c$

EVALUATION

$\displaystyle \int\limits_{}^{} \, \frac{dx}{ 4{x}^{2} - 9 }$

$= \displaystyle \frac{1}{4} \times \int\limits_{}^{} \, \frac{dx}{ {x}^{2} - \frac{9}{4} }$

$= \displaystyle \frac{1}{4} \times \int\limits_{}^{} \, \frac{dx}{ {x}^{2} - { \big( \frac{3}{2} \big)}^{2} }$

$\displaystyle = \frac{1}{4} \times \frac{1}{2 \times \frac{3}{2} } \times \log \bigg| \frac{x - \frac{3}{2} }{x + \frac{3}{2} } \bigg| + c$

$\displaystyle = \frac{1}{12} \times \log \bigg| \frac{2x - 3 }{2x + 3 } \bigg| + c$

Where C is integration constant

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