_ - 1 ^1 ( 1 + x 1 - x ) ,dx = - Vidyadip

Question

$\int_{ - 1}^1 {\log \left( {\frac{{1 + x}}{{1 - x}}} \right)\,dx = } $

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Answer

c
(c) If $f(x) = \log \left( {\frac{{1 + x}}{{1 - x}}} \right)\,,$

then $f( - x) = \log \left( {\frac{{1 - x}}{{1 + x}}} \right) = - f(x)$

Therefore, $\int_{ - 1}^1 {\log \left( {\frac{{1 + x}}{{1 - x}}} \right){\rm{ }}dx = 0} $.

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