What is the integral of 4/(x-4) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4/(x-4)

\int \frac{4}{x - 4} d x

4 ln ∣ x - 4 ∣ + C

Solution steps

\int \frac{4}{x - 4} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{x - 4} d x

Apply u-substitution

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

= 4 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 ln ∣ u ∣

Substitute back

u = x - 4

= 4 ln ∣ x - 4 ∣

Add a constant to the solution

= 4 ln ∣ x - 4 ∣ + C

\frac{156}{x}, - 49 x + 189

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

y^{^{''}} + 4 y^{^{'}} + 7 y = 0, y (0) = - 2, y^{^{'}} (0) = 4

x \to 0 - lim (e^{2 x})

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