\[\int_{{}}^{{}}{\frac{dx}{1+3{{\sin }^{2}}x}=}\] [Roorkee 1989; DCE 2001]

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

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

\[\int_{{}}^{{}}{\frac{dx}{1+3{{\sin }^{2}}x}=}\] [Roorkee 1989; DCE 2

1.	\[\int_{{}}^{{}}{\frac{dx}{1+3{{\sin }^{2}}x}=}\] [Roorkee 1989; DCE 2001]
A.	\[\frac{1}{3}{{\tan }^{-1}}(3{{\tan }^{2}}x)+c\]
B.	\[\frac{1}{2}{{\tan }^{-1}}(2\tan x)+c\]
C.	\[{{\tan }^{-1}}(\tan x)+c\]
D.	None of these
Answer» C. \[{{\tan }^{-1}}(\tan x)+c\]

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\[\int_{{}}^{{}}{\frac{dx}{1+3{{\sin }^{2}}x}=}\] [Roorkee 1989; DCE 2001]

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