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

Popular >

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

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

= \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

\int (3 + x) d x

\int p (p + 2)^{6} d p

\frac{d}{d x} (\frac{1}{x ^{2}} - \frac{3}{x ^{4}})

y = x^{4}, y = x

\frac{d}{d x} (x^{2} (3 x^{4} - 7 x + 2))

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