What is the integral of (2x-1)ln(3x) ?

The integral of (2x-1)ln(3x) is x^2ln(3x)-xln(3x)-(x^2)/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 (2x-1)ln(3x)

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

x^{2} ln (3 x) - x ln (3 x) - \frac{x ^{2}}{2} + x + C

Solution steps

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

Apply Integration By Parts

: ln (3 x) (x^{2} - x) - \int x - 1 d x

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

\int x - 1 d x = \frac{x ^{2}}{2} - x

= ln (3 x) (x^{2} - x) - (\frac{x ^{2}}{2} - x)

Simplify

ln (3 x) (x^{2} - x) - (\frac{x ^{2}}{2} - x) : x^{2} ln (3 x) - x ln (3 x) - \frac{x ^{2}}{2} + x

= x^{2} ln (3 x) - x ln (3 x) - \frac{x ^{2}}{2} + x

Add a constant to the solution

= x^{2} ln (3 x) - x ln (3 x) - \frac{x ^{2}}{2} + x + C

\int \frac{1}{( 1 - 3 x )} d x

\int x \cdot 4 x^{2} + 1 d x

\int a u d u

\int \frac{x - 7}{x ^{2} + 16} d x

\int \frac{7}{( x - 3 ) ^{2}} d x

What is the integral of (2x-1)ln(3x) ?
The integral of (2x-1)ln(3x) is x^2ln(3x)-xln(3x)-(x^2)/2+x+C