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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

integral

\frac{e ^{x}}{( 1 + e ^{x} )}

ln ∣ 1 + e^{x} ∣ + C

Solution steps

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

= ln ∣ 1 + e^{x} ∣

Add a constant to the solution

= ln ∣ 1 + e^{x} ∣ + C

in t e g r a l \frac{3}{( 2 - x ) ^{2}}

in t e g r a l \frac{1}{( x - 2 ) ^{2}}

in t e g r a l (e^{y})^{3}

in t e g r a l (sin^{2} (x)) (cos^{2} (x))

in t e g r a l (1 + x)^{4}

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