What is the integral of 1/((x+5)) ?

The integral of 1/((x+5)) is ln|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 1/((x+5))

\int \frac{1}{( x + 5 )} d x

ln ∣ x + 5 ∣ + C

Solution steps

\int \frac{1}{x + 5} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x + 5

= ln ∣ x + 5 ∣

Add a constant to the solution

= ln ∣ x + 5 ∣ + C

\int ln (x^{2} + 2 x) d x

\int \frac{3 x ^{2} + 19 x + 27}{( x + 2 ) ( x + 3 ) ^{2}} d x

\int 10 e^{- \frac{x}{2}} d x

\int (1 - x) e^{x^{2}} d x

\int (4 x^{2} - 3 x) e^{- x} d x