What is the integral of (e^{9x})/(e^{9x)+7} ?

The integral of (e^{9x})/(e^{9x)+7} is 1/9 ln|e^{9x}+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^{9x})/(e^{9x)+7}

\int \frac{e ^{9 x}}{e ^{9 x} + 7} d x

\frac{1}{9} ln e^{9 x} + 7 + C

Solution steps

\int \frac{e ^{9 x}}{e ^{9 x} + 7} d x

Apply u-substitution

: \int \frac{1}{9 u} d u

= \int \frac{1}{9 u} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{9} ln ∣ u ∣

Substitute back

u = e^{9 x} + 7

= \frac{1}{9} ln e^{9 x} + 7

Add a constant to the solution

= \frac{1}{9} ln e^{9 x} + 7 + C

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

\int (e^{9 x}) d x

\int x^{\frac{3}{4}} - \frac{1}{x ^{\frac{3}{4}}} d x

\int (x^{3} + 2 x + 1) d x

\int 7 x^{\frac{1}{2}} d x

What is the integral of (e^{9x})/(e^{9x)+7} ?
The integral of (e^{9x})/(e^{9x)+7} is 1/9 ln|e^{9x}+7|+C