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\(4{\int }_{0}^{1}\left(\frac{1}{\sqrt{3+{\mathrm{x}}^{2}}+\sqrt{1+{\mathrm{x}}^{2}}}\right)\mathrm{dx}-3{\log }_{\mathr…

Q1

\(4{\int }_{0}^{1}\left(\frac{1}{\sqrt{3+{\mathrm{x}}^{2}}+\sqrt{1+{\mathrm{x}}^{2}}}\right)\mathrm{dx}-3{\log }_{\mathrm{e}}(\sqrt{3})\) is equal to :

[JEE Main 2025, 2 Apr (Shift 2)]

a

\(2+\sqrt{2}+{\log }_{\mathrm{e}}(1+\sqrt{2})\)

b

\(2-\sqrt{2}-{\log }_{\mathrm{e}}(1+\sqrt{2})\)

c

\(2+\sqrt{2}-{\log }_{\mathrm{e}}(1+\sqrt{2})\)

d

\(2-\sqrt{2}+{\log }_{\mathrm{e}}(1+\sqrt{2})\)

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