What is the integral of (e^x)/(e^x+1) ?

The integral of (e^x)/(e^x+1) is ln|e^x+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (e^x)/(e^x+1)

\int \frac{e ^{x}}{e ^{x} + 1} d x

ln ∣ e^{x} + 1 ∣ + C

Solution steps

\int \frac{e ^{x}}{e ^{x} + 1} d x

Apply u-substitution

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = e^{x} + 1

= ln ∣ e^{x} + 1 ∣

Add a constant to the solution

= ln ∣ e^{x} + 1 ∣ + C

What is the integral of (e^x)/(e^x+1) ?
The integral of (e^x)/(e^x+1) is ln|e^x+1|+C