What is the integral of (e^x)/(-3+e^x) ?

The integral of (e^x)/(-3+e^x) is ln|-3+e^x|+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)/(-3+e^x)

\int \frac{e ^{x}}{- 3 + e ^{x}} d x

ln ∣ - 3 + e^{x} ∣ + C

Solution steps

\int \frac{e ^{x}}{- 3 + e ^{x}} 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 = - 3 + e^{x}

= ln ∣ - 3 + e^{x} ∣

Add a constant to the solution

= ln ∣ - 3 + e^{x} ∣ + C

cos^{2} (2 x)

\int 4 - e^{- x} d x

\int \frac{cos ( u )}{sin ^{2} ( u )} d u

\int \frac{x}{1 - 9 x ^{4}} d x

\int \frac{8 x - 1}{x ^{2} + x - 6} d x

What is the integral of (e^x)/(-3+e^x) ?
The integral of (e^x)/(-3+e^x) is ln|-3+e^x|+C