What is the integral of 8/(4+8x) ?

The integral of 8/(4+8x) is ln|4+8x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 8/(4+8x)

\int \frac{8}{4 + 8 x} d x

ln ∣ 4 + 8 x ∣ + C

Solution steps

\int \frac{8}{4 + 8 x} d x

Take the constant out:

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

= 8 \cdot \int \frac{1}{4 + 8 x} d x

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 = 4 + 8 x

= 8 \cdot \frac{1}{8} ln ∣ 4 + 8 x ∣

Simplify

8 \cdot \frac{1}{8} ln ∣ 4 + 8 x ∣ : ln ∣ 4 + 8 x ∣

= ln ∣ 4 + 8 x ∣

Add a constant to the solution

= ln ∣ 4 + 8 x ∣ + C

\frac{180}{x ^{7}} - \frac{4}{x ^{3}}

\frac{d y}{d x} = (e^{x} - e^{- x})^{2}

f (x) = x^{2}, (0, - 9)

sin (θ) + cos (θ)

\frac{d}{d x} (2 sec (x) tan (x))