What is the integral of (8e^{8y})/(6+e^{8y)} ?

The integral of (8e^{8y})/(6+e^{8y)} is ln|6+e^{8y}|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (8e^{8y})/(6+e^{8y)}

\int \frac{8 e ^{8 y}}{6 + e ^{8 y}} d y

ln 6 + e^{8 y} + C

Solution steps

\int \frac{8 e ^{8 y}}{6 + e ^{8 y}} d y

Take the constant out:

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

= 8 \cdot \int \frac{e ^{8 y}}{6 + e ^{8 y}} d y

Apply u-substitution

: \int \frac{1}{8 u} d u

= 8 \cdot \int \frac{1}{8 u} d u

Take the constant out:

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

= 8 \cdot \frac{1}{8} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 8 \cdot \frac{1}{8} ln ∣ u ∣

Substitute back

u = 6 + e^{8 y}

= 8 \cdot \frac{1}{8} ln 6 + e^{8 y}

Simplify

8 \cdot \frac{1}{8} ln 6 + e^{8 y} : ln 6 + e^{8 y}

= ln 6 + e^{8 y}

Add a constant to the solution

= ln 6 + e^{8 y} + C

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

2 x^{2} \cdot \frac{d y}{d x} = π y sin (\frac{π}{2 x})

x \to - 2 - lim (x^{4} + 5)

y = sin^{2} (x), y = 0

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

What is the integral of (8e^{8y})/(6+e^{8y)} ?
The integral of (8e^{8y})/(6+e^{8y)} is ln|6+e^{8y}|+C