\[\int_{{}}^{{}}{\frac{{{x}^{2}}+1}{{{x}^{4}}+1}dx=}\] [AISSE 1990]

\[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{2x} \right)+c\]

\[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{\sqrt{2x}} \right)+c\]

\[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{2\sqrt{x}} \right)+c\]

\[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{\sqrt{2}x} \right)+c\]

\[\int_{{}}^{{}}{\frac{{{x}^{2}}+1}{{{x}^{4}}+1}dx=}\] �

1.	\[\int_{{}}^{{}}{\frac{{{x}^{2}}+1}{{{x}^{4}}+1}dx=}\] [AISSE 1990]
A.	\[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{2x} \right)+c\]
B.	\[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{\sqrt{2x}} \right)+c\]
C.	\[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{2\sqrt{x}} \right)+c\]
D.	\[\frac{1}{\sqrt{2}}{{\tan }^{-1}}\left( \frac{{{x}^{2}}-1}{\sqrt{2}x} \right)+c\]
Answer» E.

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\[\int_{{}}^{{}}{\frac{{{x}^{2}}+1}{{{x}^{4}}+1}dx=}\] [AISSE 1990]

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