What is the integral of (e^{2x})/(7e^{2x)-11} ?

The integral of (e^{2x})/(7e^{2x)-11} is 1/14 ln|7e^{2x}-11|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (e^{2x})/(7e^{2x)-11}

\int \frac{e ^{2 x}}{7 e ^{2 x} - 11} d x

\frac{1}{14} ln 7 e^{2 x} - 11 + C

Solution steps

\int \frac{e ^{2 x}}{7 e ^{2 x} - 11} d x

Apply u-substitution

: \int \frac{1}{14 u} d u

= \int \frac{1}{14 u} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{14} ln ∣ u ∣

Substitute back

u = 7 e^{2 x} - 11

= \frac{1}{14} ln 7 e^{2 x} - 11

Add a constant to the solution

= \frac{1}{14} ln 7 e^{2 x} - 11 + C

\int x^{2} \cdot e^{x y} d y

\int 7 x arccos (x) d x

\int (x^{2}) 3 - 2 x d x

\int cot^{5} (3 x y) d y

\int 16 + 4 x^{2} d x

What is the integral of (e^{2x})/(7e^{2x)-11} ?
The integral of (e^{2x})/(7e^{2x)-11} is 1/14 ln|7e^{2x}-11|+C