\[\int_{{}}^{{}}{\frac{{{x}^{2}}}{({{x}^{2}}+2)({{x}^{2}}+3)}\ }dx=\] [AISSE 1990]

\[\sqrt{2}{{\tan }^{-1}}\frac{x}{\sqrt{2}}+\sqrt{3}{{\tan }^{-1}}\frac{x}{\sqrt{3}}+c\]

\[-\sqrt{2}{{\tan }^{-1}}x+\sqrt{3}{{\tan }^{-1}}x+c\]

\[-\sqrt{2}{{\tan }^{-1}}\frac{x}{\sqrt{2}}+\sqrt{3}{{\tan }^{-1}}\frac{x}{\sqrt{3}}+c\]

\[\int_{{}}^{{}}{\frac{{{x}^{2}}}{({{x}^{2}}+2)({{x}^{2}}+3)}\ }dx=\]

1.	\[\int_{{}}^{{}}{\frac{{{x}^{2}}}{({{x}^{2}}+2)({{x}^{2}}+3)}\ }dx=\] [AISSE 1990]
A.	\[-\sqrt{2}{{\tan }^{-1}}x+\sqrt{3}{{\tan }^{-1}}x+c\]
B.	\[-\sqrt{2}{{\tan }^{-1}}\frac{x}{\sqrt{2}}+\sqrt{3}{{\tan }^{-1}}\frac{x}{\sqrt{3}}+c\]
C.	\[\sqrt{2}{{\tan }^{-1}}\frac{x}{\sqrt{2}}+\sqrt{3}{{\tan }^{-1}}\frac{x}{\sqrt{3}}+c\]
D.	None of these
Answer» C. \[\sqrt{2}{{\tan }^{-1}}\frac{x}{\sqrt{2}}+\sqrt{3}{{\tan }^{-1}}\frac{x}{\sqrt{3}}+c\]

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\[\int_{{}}^{{}}{\frac{{{x}^{2}}}{({{x}^{2}}+2)({{x}^{2}}+3)}\ }dx=\] [AISSE 1990]

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