\[\int_{{}}^{{}}{\frac{{{({{\tan }^{-1}}x)}^{3}}}{1+{{x}^{2}}}\,dx=}\] [UPSEAT 2004]

\[{{({{\tan }^{-1}}x)}^{4}}+c\]

\[\frac{{{({{\tan }^{-1}}x)}^{4}}}{4}+c\]

\[2{{({{\tan }^{-1}}x)}^{2}}+c\]

\[\int_{{}}^{{}}{\frac{{{({{\tan }^{-1}}x)}^{3}}}{1+{{x}^{2}}}\,dx=}\]

1.	\[\int_{{}}^{{}}{\frac{{{({{\tan }^{-1}}x)}^{3}}}{1+{{x}^{2}}}\,dx=}\] [UPSEAT 2004]
A.	\[{{({{\tan }^{-1}}x)}^{4}}+c\]
B.	\[\frac{{{({{\tan }^{-1}}x)}^{4}}}{4}+c\]
C.	\[2{{\tan }^{-1}}x+c\]
D.	\[2{{({{\tan }^{-1}}x)}^{2}}+c\]
Answer» C. \[2{{\tan }^{-1}}x+c\]

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\[\int_{{}}^{{}}{\frac{{{({{\tan }^{-1}}x)}^{3}}}{1+{{x}^{2}}}\,dx=}\] [UPSEAT 2004]

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