The value of \[\int_{\,-\,1}^{\,3}{\,{{\tan }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right)+{{\tan }^{-1}}\left( \frac{{{x}^{2}}+1}{x} \right)\,dx}\] is [Karnataka CET 2000]

The value of \[\int_{\,-\,1}^{\,3}{\,{{\tan }^{-1}}\left( \frac{x}{{{x

1.	The value of \[\int_{\,-\,1}^{\,3}{\,{{\tan }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right)+{{\tan }^{-1}}\left( \frac{{{x}^{2}}+1}{x} \right)\,dx}\] is [Karnataka CET 2000]
A.	\[2\pi \]
B.	\[\pi \]
C.	\[\frac{21}{5}\pi \]
D.	\[\frac{\pi }{4}\]
Answer» B. \[\pi \]

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The value of \[\int_{\,-\,1}^{\,3}{\,{{\tan }^{-1}}\left( \frac{x}{{{x}^{2}}+1} \right)+{{\tan }^{-1}}\left( \frac{{{x}^{2}}+1}{x} \right)\,dx}\] is [Karnataka CET 2000]

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