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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

ln e^{t} + 1 + C

Solution steps

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

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 = e^{t} + 1

= ln e^{t} + 1

Add a constant to the solution

= ln e^{t} + 1 + C

\int - 8 cos (x) d x

\int ln (sec (x)) tan (x) d x

\int sin^{10} (x) cos^{7} (x) d x

\int e^{- s t} ln (t) d t

\int \frac{8 x ^{7}}{x ^{8} + 1} d x

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