What is the integral of ln(4-2x) ?

The integral of ln(4-2x) is xln(4-2x)-2ln|2-x|-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(4-2x)

\int ln (4 - 2 x) d x

x ln (4 - 2 x) - 2 ln ∣ 2 - x ∣ - x + C

Solution steps

\int ln (4 - 2 x) d x

Apply Integration By Parts

: x ln (4 - 2 x) - \int - \frac{x}{2 - x} d x

= x ln (4 - 2 x) - \int - \frac{x}{2 - x} d x

\int - \frac{x}{2 - x} d x = 2 ln ∣ 2 - x ∣ + x

= x ln (4 - 2 x) - (2 ln ∣ 2 - x ∣ + x)

Simplify

= x ln (4 - 2 x) - 2 ln ∣ 2 - x ∣ - x

Add a constant to the solution

= x ln (4 - 2 x) - 2 ln ∣ 2 - x ∣ - x + C

\int 10 cos (x) + sec^{2} (x) d x

\int 18 csc^{2} (9 x) cot (9 x) d x

\int \frac{1}{( 2 x + 2 ) ( ln ( x + 1 ) ) ^{2}} d x

\int \frac{cos ( 2 x )}{2 + 3 sin ( 2 x )} d x

\int 2 e^{t} + 3 sin (t) d t

What is the integral of ln(4-2x) ?
The integral of ln(4-2x) is xln(4-2x)-2ln|2-x|-x+C