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

x \to 8 lim (\frac{( 1 )}{( x - 8 )})

\frac{\partial}{\partial y} (arcsin (x y))

\int \frac{1}{x ^{2} - 4 x + 9} d x

f (x) = 6 x - x^{2}, at x = 1

z \to 0 lim (\frac{- 1}{z})

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