Question

$\int \frac{dx}{e^x+e^{-x}+2}$ is equal to

• A. $\frac{1}{e^x+1}+C$
• B. $\frac{-1}{e^x+1}+C$
• C. $\frac{1}{1+e^{-x}}+C$
• D. $\frac{1}{e^{-x}-1}+C$
• E. $\frac{1}{e^x-1}+C$

Answer 1

Answer: (B)

Let $I=\int \frac{dx}{e^x+e^{-x}+2}$
$=\int \frac{e^x}{e^{2x}+2e^x+1}dx$
Put $e^x=t$
$\Rightarrow e^{x}dx=dt$
$\therefore I=\int \frac{dt}{t^2+2t+1}$
$=\int \frac{dt}{(t+1{)}^2}$
$=\frac{-1}{t+1}+C$
$=\frac{-1}{e^x+1}+C$