\[\int_{{}}^{{}}{\frac{dx}{1+x+{{x}^{2}}+{{x}^{3}}}=}\] [MP PET 1991]

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

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

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

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

\[\int_{{}}^{{}}{\frac{dx}{1+x+{{x}^{2}}+{{x}^{3}}}=}\] [MP PET

1.	\[\int_{{}}^{{}}{\frac{dx}{1+x+{{x}^{2}}+{{x}^{3}}}=}\] [MP PET 1991]
A.	\[\log \sqrt{1+x}-\frac{1}{2}\log \sqrt{1+{{x}^{2}}}+\frac{1}{2}{{\tan }^{-1}}x+c\]
B.	\[\log \sqrt{1+x}-\log \sqrt{1+{{x}^{2}}}+{{\tan }^{-1}}x+c\]
C.	\[\log \sqrt{1+{{x}^{2}}}-\log \sqrt{1+x}+\frac{1}{2}{{\tan }^{-1}}x+c\]
D.	\[\log \sqrt{1+x}+{{\tan }^{-1}}x+\log \sqrt{1+{{x}^{2}}}+c\]
Answer» B. \[\log \sqrt{1+x}-\log \sqrt{1+{{x}^{2}}}+{{\tan }^{-1}}x+c\]

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\[\int_{{}}^{{}}{\frac{dx}{1+x+{{x}^{2}}+{{x}^{3}}}=}\] [MP PET 1991]

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