What is the integral of (e^x)/(5+e^x) ?

The integral of (e^x)/(5+e^x) is ln|5+e^x|+C

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integral of (e^x)/(5+e^x)

\int \frac{e ^{x}}{5 + e ^{x}} d x

ln ∣ 5 + e^{x} ∣ + C

Solution steps

\int \frac{e ^{x}}{5 + 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 = 5 + e^{x}

= ln ∣ 5 + e^{x} ∣

Add a constant to the solution

= ln ∣ 5 + e^{x} ∣ + C

n = 1 \sum \infty \frac{n ^{5}}{4 ^{n}}

\int_{2}^{\infty} 0 d x

\int - F x - x d x

\int \frac{cos ( θ )}{sin ^{2} ( θ )} d θ

\frac{\partial}{\partial x} (\frac{2 x - 2 y}{y ^{2} + 4 x ^{2}})

What is the integral of (e^x)/(5+e^x) ?
The integral of (e^x)/(5+e^x) is ln|5+e^x|+C