\[\int_{{}}^{{}}{\frac{dx}{x({{x}^{n}}+1)}=}\] [Roorkee 1979]

\[\frac{1}{n}\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\]

\[n\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\]

\[n\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\]

\[\frac{1}{n}\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\]

\[\int_{{}}^{{}}{\frac{dx}{x({{x}^{n}}+1)}=}\] [Roor

1.	\[\int_{{}}^{{}}{\frac{dx}{x({{x}^{n}}+1)}=}\] [Roorkee 1979]
A.	\[n\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\]
B.	\[n\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\]
C.	\[\frac{1}{n}\log \frac{{{x}^{n}}}{{{x}^{n}}+1}+c\]
D.	\[\frac{1}{n}\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\]
Answer» D. \[\frac{1}{n}\log \frac{{{x}^{n}}+1}{{{x}^{n}}}+c\]

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\[\int_{{}}^{{}}{\frac{dx}{x({{x}^{n}}+1)}=}\] [Roorkee 1979]

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