What is the integral of (e^x)/(e^x+2) ?

The integral of (e^x)/(e^x+2) is ln|e^x+2|+C

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integral of (e^x)/(e^x+2)

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

ln ∣ e^{x} + 2 ∣ + C

Solution steps

\int \frac{e ^{x}}{e ^{x} + 2} 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} + 2

= ln ∣ e^{x} + 2 ∣

Add a constant to the solution

= ln ∣ e^{x} + 2 ∣ + C

\frac{d}{d x} (\frac{5 - 3 x}{x ^{2} + 3 x})

cos (\frac{π x}{2})

\int_{0}^{1} 4 x arccos (x) d x

\int \frac{13 x ^{3}}{2 + x ^{2}} d x

sin ((π x)^{3})

What is the integral of (e^x)/(e^x+2) ?
The integral of (e^x)/(e^x+2) is ln|e^x+2|+C