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))

integral

\frac{e ^{x}}{( e ^{x} + 2 )}

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

2 x (4 - x^{2})

\frac{1}{( x ^{- 0} 0.5 + x ^{0.5} )}

\frac{e ^{1}}{e ^{x} + 1}

\frac{ln ( 1 + x ^{2} )}{x ^{2}}

\frac{1}{t ^{2}}

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