# Integrate : $\int \limits_3^5 \large\frac{\sqrt {\log (x)}}{\log (\theta- x)+ \log (x)}$$dx $\begin {array} {1 1} (a)\;\frac{5}{2} \\ (b)\;\frac{3}{2} \\ (c)\;1 \\ (d)\;\frac{5}{4} \end {array}$ ## 1 Answer \int \limits_a^b \large\frac{f(x)}{f(a+b-x)+f(x)}$$dx=\large\frac{b-a}{2}$
By using the above formula
$a=3, b=5$
$a+b=8$
$\large\frac{b-a}{2}=\frac{5-3}{2}=1$
Hence the correct answer is c