What is the integral of (e^t)/(e^t-2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (e^t)/(e^t-2)

\int \frac{e ^{t}}{e ^{t} - 2} d t

ln e^{t} - 2 + C

Solution steps

\int \frac{e ^{t}}{e ^{t} - 2} d t

Apply u-substitution

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = e^{t} - 2

= ln e^{t} - 2

Add a constant to the solution

= ln e^{t} - 2 + C

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