What is the integral of 7/(x+5) ?

The integral of 7/(x+5) is 7ln|x+5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 7/(x+5)

\int \frac{7}{x + 5} d x

7 ln ∣ x + 5 ∣ + C

Solution steps

\int \frac{7}{x + 5} d x

Take the constant out:

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

= 7 \cdot \int \frac{1}{x + 5} d x

Apply u-substitution

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

= 7 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 7 ln ∣ u ∣

Substitute back

u = x + 5

= 7 ln ∣ x + 5 ∣

Add a constant to the solution

= 7 ln ∣ x + 5 ∣ + C

\int x coth (x^{2}) d x

\int x (x^{2} + 1)^{\frac{3}{4}} d x

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

\int sinh (x) (cosh (x))^{2} d x

\int 2^{x} \cdot 2^{2^{x}} d x