What is the integral of 3ln(2x) ?

The integral of 3ln(2x) is 3(xln(2x)-x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3ln(2x)

\int 3 ln (2 x) d x

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

Solution steps

\int 3 ln (2 x) d x

Take the constant out:

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

= 3 \cdot \int ln (2 x) d x

Apply Integration By Parts

: x ln (2 x) - \int 1 d x

= 3 (x ln (2 x) - \int 1 d x)

\int 1 d x = x

= 3 (x ln (2 x) - x)

Add a constant to the solution

= 3 (x ln (2 x) - x) + C

\int \frac{3 x}{3} d x

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

\int \frac{5 + sec ^{2} ( x )}{5 x + tan ( x )} d x

\int sin (x) - sec (x) tan (x) d x

\int \frac{x ^{3} + 2}{x + 1} d x