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

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

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

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

ln ∣ e^{x} + e ∣ + C

Solution steps

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

= ln ∣ e^{x} + e ∣

Add a constant to the solution

= ln ∣ e^{x} + e ∣ + C

\int \frac{1}{y} d y

\frac{1}{2 x + 1}

\int_{- π}^{2 π} π cos^{2} (x) d x

f (x) = 3 x^{2} e^{x} + e^{x} (x^{3} + 2)

\int \frac{49 + x ^{2}}{x} d x

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