What is the integral of (e^x)/(6+e^x) ?

The integral of (e^x)/(6+e^x) is ln|6+e^x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (e^x)/(6+e^x)

\int \frac{e ^{x}}{6 + e ^{x}} d x

ln ∣ 6 + e^{x} ∣ + C

Solution steps

\int \frac{e ^{x}}{6 + e ^{x}} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 6 + e^{x}

= ln ∣ 6 + e^{x} ∣

Add a constant to the solution

= ln ∣ 6 + e^{x} ∣ + C

\int_{- 1}^{1} e^{y} - (y^{2} - 5) d y

\int_{1}^{5} (2 x - 1) d x

\int \frac{3 x}{2} d x

\int \frac{x ^{2}}{( 81 + x ^{2} ) ^{2}} d x

\frac{d}{d t} (ln (1 + t^{2}))

What is the integral of (e^x)/(6+e^x) ?
The integral of (e^x)/(6+e^x) is ln|6+e^x|+C