A) \[\log \sqrt{{{x}^{2}}-4x+3}+c\]
B) \[x\log (x-3)-2\log (x-2)+c\]
C) \[\log [(x-3)(x-1)]\]
D) None of these
Correct Answer: A
Solution :
Put \[{{x}^{2}}-4x+3=t\Rightarrow (2x-4)\,dx=dt\] \[\Rightarrow (x-2)\,dx=\frac{1}{2}dt,\] then it reduces to \[\frac{1}{2}\int_{{}}^{{}}{\frac{dt}{t}=\frac{1}{2}\log t+c=\frac{1}{2}\log ({{x}^{2}}-4x+3)+c.}\]
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