What is the integral of 1/((1+1/2 x)) ?

The integral of 1/((1+1/2 x)) is 2ln|1+1/2 x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((1+1/2 x))

integral

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

2 ln 1 + \frac{1}{2} x + C

Solution steps

\int \frac{1}{1 + \frac{1}{2} x} d x

Apply u-substitution

: \int \frac{2}{u} d u

= \int \frac{2}{u} d u

Take the constant out:

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

= 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = 1 + \frac{1}{2} x

= 2 ln 1 + \frac{1}{2} x

Add a constant to the solution

= 2 ln 1 + \frac{1}{2} x + C

\frac{cos ^{23} ( x )}{sin ( x )}

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

2 x (1 - x^{- 3})

\frac{3}{4} - \frac{x}{4}

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

What is the integral of 1/((1+1/2 x)) ?
The integral of 1/((1+1/2 x)) is 2ln|1+1/2 x|+C