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

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

integral

\frac{5}{x + 1}

5 ln ∣ x + 1 ∣ + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 5 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 ln ∣ u ∣

Substitute back

u = x + 1

= 5 ln ∣ x + 1 ∣

Add a constant to the solution

= 5 ln ∣ x + 1 ∣ + C

\frac{( 1 + x ) ^{2}}{x ^{2}}

\frac{( 1 - x ^{2} )}{( e ^{2} x )}

\frac{x ^{- 2}}{3}

sin (2 x) + cos (x)

\frac{1}{( x ^{2} + y ^{2} + z ^{2} )}