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Find the integral value
Answer
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$\dfrac {1} {4} \times \ln{\left( |\dfrac {x - 2} {x + 2}| \right)} + C$
Find the integral value
$\color{#FF6800}{\int \dfrac {1} {x ^ {2} - 4}dx}$
$ $ Using $ \int \dfrac {1} {x ^ {2} - a ^ {2}}dx = \dfrac {1} {2 \times a} \times \ln{\left( |\dfrac {x - a} {x + a}| \right)} $ , calculate the integral $ $
$\color{#FF6800}{\dfrac {1} {2 \times 2} \times \ln }{\left( \color{#FF6800}{|\dfrac {x - 2} {x + 2}|} \right)} \color{#FF6800}{}$
$\dfrac {1} {2 \times 2} \times \ln{\left( |\dfrac {x - 2} {x + 2}| \right)}$
$ $ Multiply the numbers $ $
$\dfrac {1} {4} \times \ln{\left( |\dfrac {x - 2} {x + 2}| \right)}$
$\color{#FF6800}{\dfrac {1} {4} \times \ln }{\left( \color{#FF6800}{|\dfrac {x - 2} {x + 2}|} \right)} \color{#FF6800}{}$
$ $ Add integral constant $ C \in ℝ $ $ $
$\color{#FF6800}{\dfrac {1} {4} \times \ln }{\left( \color{#FF6800}{|\dfrac {x - 2} {x + 2}|} \right)} \color{#FF6800}{ + C}$
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