A) \[2/3\]
B) \[1/3\]
C) \[3/2\]
D) In 2
Correct Answer: A
Solution :
Let \[I=\int_{1}^{{{e}^{2}}}{\frac{dx}{x{{(1+\log x)}^{2}}}}\] Put \[1+\log \,x=t\] \[\Rightarrow \] \[\frac{1}{x}dx=dt\] when \[x=1,\,t=1\] and \[x={{e}^{2}},t=3\] \[\therefore \] \[I=\int_{1}^{3}{\frac{1}{{{t}^{2}}}dt}\] \[=\left[ -\frac{1}{t} \right]_{1}^{3}=-\frac{1}{3}+1=\frac{2}{3}\]You need to login to perform this action.
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