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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int \frac{x + 3}{x ^{2} + 2 x + 1} d x

\int x + \frac{1}{8 x} d x

\int 18 (3 x + 2)^{2} d x

\int \frac{5 x - 3}{x ^{2} + 8 x + 7} d x

\int 12 x^{- 1} d x

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