What is the integral of (e^{7x})/(e^{7x)+4} ?

The integral of (e^{7x})/(e^{7x)+4} is 1/7 ln|e^{7x}+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^{7x})/(e^{7x)+4}

\int \frac{e ^{7 x}}{e ^{7 x} + 4} d x

\frac{1}{7} ln e^{7 x} + 4 + C

Solution steps

\int \frac{e ^{7 x}}{e ^{7 x} + 4} d x

Apply u-substitution

: \int \frac{1}{7 u} d u

= \int \frac{1}{7 u} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{7} ln ∣ u ∣

Substitute back

u = e^{7 x} + 4

= \frac{1}{7} ln e^{7 x} + 4

Add a constant to the solution

= \frac{1}{7} ln e^{7 x} + 4 + C

\int \frac{( x + 1 )}{4 - x ^{2}} d x

\int \frac{x + 3 - 2}{x - 1} d x

\int \frac{1}{3 x + 10} d x

\int x cos (x + 2) d x

\int \frac{2 x + 4}{x ^{2} - 10 x + 16} d x

What is the integral of (e^{7x})/(e^{7x)+4} ?
The integral of (e^{7x})/(e^{7x)+4} is 1/7 ln|e^{7x}+4|+C