A) \[\log ({{x}^{4}}+1)+c\]
B) \[\frac{1}{4}\log ({{x}^{4}}+1)+c\]
C) \[-\log ({{x}^{4}}+1)+c\]
D) None of these
Correct Answer: B
Solution :
\[I=\int{{{e}^{3\log x}}{{({{x}^{4}}+1)}^{-1}}dx}\]\[=\int{{{e}^{\log {{x}^{3}}}}{{({{x}^{4}}+1)}^{-1}}dx}\] \[=\frac{1}{4}\int{\frac{4{{x}^{3}}}{({{x}^{4}}+1)}dx}=\frac{1}{4}\log ({{x}^{4}}+1)+c\].
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