What is the integral of k/(x+1) ?

The integral of k/(x+1) is kln|x+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of k/(x+1)

\int \frac{k}{x + 1} d x

k ln ∣ x + 1 ∣ + C

Solution steps

\int \frac{k}{x + 1} d x

Take the constant out:

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

= k \cdot \int \frac{1}{x + 1} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= k ln ∣ u ∣

Substitute back

u = x + 1

= k ln ∣ x + 1 ∣

Add a constant to the solution

= k ln ∣ x + 1 ∣ + C

\int_{0}^{5} 12 \frac{t}{t + 1} d t

\int csc (9 x) d x

\int \frac{3 x}{x + 4} d x

\int y^{2} + 4 d y

x sin (x)