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

integral of ln(2+x)

integral

ln (2 + 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

Apply Integration By Parts

= 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

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