What is the integral of 1/((4-x)) ?

The integral of 1/((4-x)) is -ln|4-x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((4-x))

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

- ln ∣ 4 - x ∣ + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = 4 - x

= - ln ∣ 4 - x ∣

Add a constant to the solution

= - ln ∣ 4 - x ∣ + C

\int 3 x x - 1 d x

\int 3 x x - 2 d x

\int 9 x^{2} 1 + 2 x^{3} d x

\int p (p + 8)^{7} d p

\int (2 x + 3) e^{x^{2} + 3 x} d x