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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/((1+4 x/l))

integral

\frac{1}{( 1 + 4 \frac{x}{l} )}

\frac{l}{4} ln 1 + \frac{4 x}{l} + C

Solution steps

\int \frac{1}{1 + 4 \cdot \frac{x}{l}} d x

Apply u-substitution

= \int \frac{l}{4 u} d u

Take the constant out:

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

= \frac{l}{4} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{l}{4} ln ∣ u ∣

Substitute back

u = 1 + 4 \cdot \frac{x}{l}

= \frac{l}{4} ln 1 + 4 \cdot \frac{x}{l}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{l}{4} ln 1 + \frac{4 x}{l}

Add a constant to the solution

= \frac{l}{4} ln 1 + \frac{4 x}{l} + C

What is the integral of 1/((1+4 x/l)) ?
The integral of 1/((1+4 x/l)) is l/4 ln|1+(4x)/l |+C