What is the integral of ln(2+x) ?

The integral of ln(2+x) is 2ln(2+x)+xln(2+x)-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 ln(2+x)

\int ln (2 + x) d x

2 ln (2 + x) + x ln (2 + x) - 2 - x + C

Solution steps

\int ln (2 + x) d x

Apply u-substitution

: \int ln (u) d u

= \int ln (u) d u

Apply Integration By Parts

: u ln (u) - \int 1 d u

= u ln (u) - \int 1 d u

\int 1 d u = u

= u ln (u) - u

Substitute back

u = 2 + x

= (2 + x) ln (2 + x) - (2 + x)

Simplify

(2 + x) ln (2 + x) - (2 + x) : 2 ln (2 + x) + x ln (2 + x) - 2 - x

= 2 ln (2 + x) + x ln (2 + x) - 2 - x

Add a constant to the solution

= 2 ln (2 + x) + x ln (2 + x) - 2 - x + C

(- 1, 1), (1, - 2)

x \to 0 lim (\frac{tan ( 2 ) ( x )}{x})

2 x^{8} e^{x}

\int \frac{1}{4 x} d x

\frac{d}{d x} (4 x^{3} + 5 x)

What is the integral of ln(2+x) ?
The integral of ln(2+x) is 2ln(2+x)+xln(2+x)-2-x+C