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

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

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

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

ln 1 + e^{t} + C

Solution steps

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

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^{t}

= ln 1 + e^{t}

Add a constant to the solution

= ln 1 + e^{t} + C

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