\(\int\dfrac{x+3}{4-x^2}dx=\int\dfrac{-x-3}{\left(x-2\right)\left(x+2\right)}dx=\dfrac{1}{4}\int\dfrac{-4x-12}{\left(x-2\right)\left(x+2\right)}dx\)
\(=\dfrac{1}{4}\int\left(\dfrac{\left(x-2\right)-5\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\right)dx\)
\(=\dfrac{1}{4}\int\left(\dfrac{1}{x+2}-\dfrac{5}{x-2}\right)dx\)
\(=\dfrac{1}{4}ln\left|x+2\right|-\dfrac{5}{4}ln\left|x-2\right|+C\)
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