What is the integral of (e^{5x})/(e^{5x)-4} ?

The integral of (e^{5x})/(e^{5x)-4} is 1/5 ln|e^{5x}-4|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (e^{5x})/(e^{5x)-4}

\int \frac{e ^{5 x}}{e ^{5 x} - 4} d x

\frac{1}{5} ln e^{5 x} - 4 + C

Solution steps

\int \frac{e ^{5 x}}{e ^{5 x} - 4} d x

Apply u-substitution

: \int \frac{1}{5 u} d u

= \int \frac{1}{5 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} ln ∣ u ∣

Substitute back

u = e^{5 x} - 4

= \frac{1}{5} ln e^{5 x} - 4

Add a constant to the solution

= \frac{1}{5} ln e^{5 x} - 4 + C

\int \frac{1}{6 - 5 x} d x

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

\int e^{- x} (x^{2} + 5) d x

\int \frac{1}{R ^{2}} d R

\int \frac{2}{x ^{2} - x - 30} d x

What is the integral of (e^{5x})/(e^{5x)-4} ?
The integral of (e^{5x})/(e^{5x)-4} is 1/5 ln|e^{5x}-4|+C