What is the integral of (2x+1)*ln(x) ?

The integral of (2x+1)*ln(x) is x^2ln(x)+xln(x)-(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(x)

\int (2 x + 1) \cdot ln (x) d x

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

Solution steps

\int (2 x + 1) ln (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

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

Add a constant to the solution

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

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

\int 4 y + 2 t - 5 d t

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

\int x^{23} d x

\int (10 x^{4} - 18 x^{2} + 2 x + 3) d x

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