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

\int 2 x (x^{2} + 14)^{9} d x

\frac{( d y )}{( d x )} = \frac{x}{y}

\int_{1}^{2} (ln (x))^{2} d x

y = - x, x = - 1, x = 2, y = 0

y^{^{''}} + 8 y^{^{'}} + 65 y = 455, y (0) = 0, y^{^{'}} (0) = 0

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