A) \[{{e}^{3\log x}}+c\]
B) \[\frac{1}{4}\log ({{x}^{4}}+1)+c\]
C) \[\log ({{x}^{4}}+1)+c\]
D) \[\frac{1}{2}\log ({{x}^{4}}+1)+c\]
E) \[\frac{{{x}^{4}}}{{{x}^{4}}+1}+c\]
Correct Answer: B
Solution :
\[\int{{{e}^{3\log x}}}{{({{x}^{4}}+1)}^{-1}}dx\] \[=\int{\frac{{{x}^{3}}}{1+{{x}^{4}}}}dx=\frac{1}{4}\log ({{x}^{4}}+1)+c\]
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