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The value of integral \({\int }_{0}^{\infty }\frac{6}{{e}^{3x}+6{e}^{2x}+11{e}^{x}+6}dx=\) [JEE Main 2023, 13 Apr (Shift…

Q1

The value of integral \({\int }_{0}^{\infty }\frac{6}{{e}^{3x}+6{e}^{2x}+11{e}^{x}+6}dx=\)

[JEE Main 2023, 13 Apr (Shift 1)]

a

\({\log }_{e}\left(\frac{512}{81}\right)\)

b

\({\log }_{e}\left(\frac{32}{27}\right)\)

c

\({{\log }_{e}}_{,}\left(\frac{256}{81}\right)\)

d

\({\log }_{e}\left(\frac{64}{27}\right)\)

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