\[\int_{{}}^{{}}{\frac{dx}{4{{x}^{2}}+9}=}\] [MP PET 1991; Roorkee 1977; MNR 1974]

\[\frac{1}{6}{{\tan }^{-1}}\left( \frac{3x}{2} \right)+c\]

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

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

\[\frac{1}{6}{{\tan }^{-1}}\left( \frac{2x}{3} \right)+c\]

\[\frac{1}{6}{{\tan }^{-1}}\left( \frac{3x}{2} \right)+c\]

\[\int_{{}}^{{}}{\frac{dx}{4{{x}^{2}}+9}=}\] [MP PET 1991; Roorkee 197

1.	\[\int_{{}}^{{}}{\frac{dx}{4{{x}^{2}}+9}=}\] [MP PET 1991; Roorkee 1977; MNR 1974]
A.	\[\frac{1}{2}{{\tan }^{-1}}\left( \frac{2x}{3} \right)+c\]
B.	\[\frac{3}{2}{{\tan }^{-1}}\left( \frac{2x}{3} \right)+c\]
C.	\[\frac{1}{6}{{\tan }^{-1}}\left( \frac{2x}{3} \right)+c\]
D.	\[\frac{1}{6}{{\tan }^{-1}}\left( \frac{3x}{2} \right)+c\]
Answer» D. \[\frac{1}{6}{{\tan }^{-1}}\left( \frac{3x}{2} \right)+c\]