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

The integral of x^2ln(2x+1) is 1/3 x^3ln(2x+1)-1/72 (8x^3-6x^2+6x-3ln|2x+1|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^2ln(2x+1)

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

\frac{1}{3} x^{3} ln (2 x + 1) - \frac{1}{72} (8 x^{3} - 6 x^{2} + 6 x - 3 ln ∣ 2 x + 1 ∣) + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{2 x ^{3}}{3 ( 2 x + 1 )} d x = \frac{1}{72} (8 x^{3} - 6 x^{2} + 6 x - 3 ln ∣ 2 x + 1 ∣)

= \frac{1}{3} x^{3} ln (2 x + 1) - \frac{1}{72} (8 x^{3} - 6 x^{2} + 6 x - 3 ln ∣ 2 x + 1 ∣)

Add a constant to the solution

= \frac{1}{3} x^{3} ln (2 x + 1) - \frac{1}{72} (8 x^{3} - 6 x^{2} + 6 x - 3 ln ∣ 2 x + 1 ∣) + C

\int \frac{1}{9 + 4 v ^{2}} d v

\int \frac{x ^{2} + 1}{x ^{3} + 9 x} d x

\int (16 x^{3} - 14 x + 6) d x

\int 6^{x} x d x

\int \frac{9}{1 + 9 x ^{2}} d x

What is the integral of x^2ln(2x+1) ?
The integral of x^2ln(2x+1) is 1/3 x^3ln(2x+1)-1/72 (8x^3-6x^2+6x-3ln|2x+1|)+C