What is the integral of (e^x)/(4+e^x) ?

The integral of (e^x)/(4+e^x) is ln|4+e^x|+C

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integral of (e^x)/(4+e^x)

\int \frac{e ^{x}}{4 + e ^{x}} d x

ln ∣ 4 + e^{x} ∣ + C

Solution steps

\int \frac{e ^{x}}{4 + 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 = 4 + e^{x}

= ln ∣ 4 + e^{x} ∣

Add a constant to the solution

= ln ∣ 4 + e^{x} ∣ + C

\frac{d}{d t} (t^{2} + 1)

\frac{d y}{d t} = \frac{t ^{2}}{y ( 1 + t ^{3} )}

\int_{3}^{4} \frac{x}{8} d x

\frac{\partial}{\partial r} (π r^{2} h)

\frac{11}{x}

What is the integral of (e^x)/(4+e^x) ?
The integral of (e^x)/(4+e^x) is ln|4+e^x|+C