A) \[\frac{x}{{{(\log \,x)}^{2}}+1}+C\]
B) \[\frac{x{{e}^{x}}}{1+\,{{x}^{2}}}+C\]
C) \[\frac{x}{\,{{x}^{2}}+1}+C\]
D) \[\frac{\log \,\,x}{\,{{(\log x)}^{2}}+1}+C\]
Correct Answer: A
Solution :
Let\[l=\int_{{}}^{{}}{{{\left[ \frac{\log x-1}{1+{{(\log x)}^{2}}} \right]}^{2}}dx}\] \[=\frac{x}{1+{{(\log x)}^{2}}}+\int{\frac{2\log x}{{{[1+{{(\log x)}^{2}}]}^{2}}}}dx\] \[-\int{\frac{2\log x}{{{[1+{{(\log x)}^{2}}]}^{2}}}}dx\] \[=\frac{x}{1+{{(\log x)}^{2}}}+C\]You need to login to perform this action.
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