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Question

Let $f(x) = \int {{{2x} \over {({x^2} + 1)({x^2} + 3)}}dx} $. If $f(3) = {1 \over 2}({\log _e}5 - {\log _e}6)$, then $f(4)$ is equal to

${\log _e}19 - {\log _e}20$
${\log _e}17 - {\log _e}18$
${1 \over 2}({\log _e}19 - {\log _e}17)$
${1 \over 2}({\log _e}17 - {\log _e}19)$

Solution

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