What is the integral of (e^x)/(e^x-7) ?

The integral of (e^x)/(e^x-7) is ln|e^x-7|+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-7)

\int \frac{e ^{x}}{e ^{x} - 7} d x

ln ∣ e^{x} - 7 ∣ + C

Solution steps

\int \frac{e ^{x}}{e ^{x} - 7} 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} - 7

= ln ∣ e^{x} - 7 ∣

Add a constant to the solution

= ln ∣ e^{x} - 7 ∣ + C

\int 7 x (x^{2} + 5)^{4} d x

\int e^{3 x} 1 + e^{3 x} d x

\int \frac{1}{4 u} d u

\int \frac{x - 1}{x ^{2}} e^{x} d x

\int sec^{2} (4 x) tan (4 x) d x

What is the integral of (e^x)/(e^x-7) ?
The integral of (e^x)/(e^x-7) is ln|e^x-7|+C