0 6 e 3 x + 6 e 2 x + 11 e x + 6 d x = [2023]

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Solution

Q.
$\int_{0}^{\infty} \frac{6}{e^{3 x} + 6 e^{2 x} + 11 e^{x} + 6} d x =$ [2023]

1 $\log_{e} (\frac{64}{27})$

2 $\log_{e} (\frac{512}{81})$

3 $\log_{e} (\frac{256}{81})$

4 $\log_{e} (\frac{32}{27})$

Ans.
(4)

Put $e^{x} = t \Rightarrow e^{x} d x = d t$ and on solving, we get $\log_{e} (\frac{32}{27})$

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