What is the integral of (e^{5x})/(9+e^{5x)} ?

The integral of (e^{5x})/(9+e^{5x)} is 1/5 ln|9+e^{5x}|+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})/(9+e^{5x)}

\int \frac{e ^{5 x}}{9 + e ^{5 x}} d x

\frac{1}{5} ln 9 + e^{5 x} + C

Solution steps

\int \frac{e ^{5 x}}{9 + e ^{5 x}} 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 = 9 + e^{5 x}

= \frac{1}{5} ln 9 + e^{5 x}

Add a constant to the solution

= \frac{1}{5} ln 9 + e^{5 x} + C

\int x ln (x) + 1 d x

\int \frac{v}{4 + v ^{2}} d v

\int x^{4} (x^{5} - 1)^{7} d x

\int \frac{12 x ^{3}}{x ^{4} + 9} d x

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

What is the integral of (e^{5x})/(9+e^{5x)} ?
The integral of (e^{5x})/(9+e^{5x)} is 1/5 ln|9+e^{5x}|+C