First slide

Methods of integration

Question

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

Easy

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

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

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App