∫dxex+e−x+2 is equal to - Infinity Learn by Sri Chaitanya

A
$\frac{1}{e^{x} + 1} + C$
B
$- \frac{1}{e^{x} + 1} + C$
C
$\frac{1}{1 + e^{- x}} + C$
D
None of these

Solution:

$\begin{aligned} I = \int \frac{dx}{e^{x} + e^{- x} + 2} = \int \frac{e^{x} dx}{e^{2 x} + 2 e^{x} + 1} \\ = \int \frac{e^{x}}{{(e^{x} + 1)}^{2}} dx = - \frac{1}{e^{x} + 1} + C \end{aligned}$

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