What is the integral of (e^x)/(3+e^x) ?

The integral of (e^x)/(3+e^x) is ln|3+e^x|+C

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integral of (e^x)/(3+e^x)

\int \frac{e ^{x}}{3 + e ^{x}} d x

ln ∣ 3 + e^{x} ∣ + C

Solution steps

\int \frac{e ^{x}}{3 + 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 = 3 + e^{x}

= ln ∣ 3 + e^{x} ∣

Add a constant to the solution

= ln ∣ 3 + e^{x} ∣ + C

\int ln (13 t) d t

\int r^{2} (r^{3} - 2)^{2} d r

H (- 5) = 2^{x}

\frac{d}{d x} (\frac{( x + 1 )}{x})

\frac{d}{d x} (3500 (1 - \frac{1}{50} x)^{2})

What is the integral of (e^x)/(3+e^x) ?
The integral of (e^x)/(3+e^x) is ln|3+e^x|+C