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

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

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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

y = 4 t t + 7

\int_{- 2}^{2} x^{2} - 1 d x

f (x) = 2 e^{- x}

\int 4 sin^{4} (x) cos^{2} (x) d x

\frac{1}{2 + 5 x}

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