A) \[\log (2/3)\]
B) \[\log (1/4)\]
C) \[\log (4/3)\]
D) \[\log (8/3)\]
Correct Answer: C
Solution :
\[I=\int_{2}^{3}{\frac{dx}{{{x}^{2}}-x}}\]\[=\int_{2}^{3}{\frac{dx}{x\,(x-1)}}\]\[=\int_{2}^{3}{\left[ \frac{1}{x-1}-\frac{1}{x} \right]}\,dx\] \[=\int_{2}^{3}{\frac{1}{(x-1)}}\,dx-\int_{2}^{3}{\frac{1}{x}dx}\]\[=[\log (x-1)]_{2}^{3}-[\log x]_{2}^{3}\] \[=[\log 2-\log 1]-[\log 3-\log 2]\]\[=2\log 2-\log 3=\log \frac{4}{3}\].
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