_ 2 - 3 ^ 3 + 3 (4 + x) (4 + x) + (9 - x) , ,dx = - Vidyadip

MCQ

$\int\limits_{2 - \log 3}^{3 + \log 3} {\frac{{\log (4 + x)}}{{\log (4 + x) + \log (9 - x)}}\,\,dx = } $

✓
$\frac{1}{2} + log\, 3$
B
$\frac{5}{2}$
C
$1 + 2\, log \,3$
D
None of these

✓

Answer

Correct option: A.

$\frac{1}{2} + log\, 3$

a
$\int_{2-\log 3}^{3+\log 3} \frac{\log (4+x) d x}{\log (4+x)+\log (4+5-x)}$

$=\frac{3+\log 3-(2-\log 3)}{2}$

$=\frac{1+2 \log 3}{2}$

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