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

The integral of (x^2(ln(x))^2) is 1/3 x^3ln^2(x)-2/3 (1/3 x^3ln(x)-(x^3)/9)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{3} x^{3} ln^{2} (x) - \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{2}{3} x^{2} ln (x) d x = \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

= \frac{1}{3} x^{3} ln^{2} (x) - \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Add a constant to the solution

= \frac{1}{3} x^{3} ln^{2} (x) - \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

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

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

\int x 5 x^{2} + 3 d x

\int \frac{ln ( y )}{y ^{2}} d y

\int 6 + cos (x) d x

What is the integral of (x^2(ln(x))^2) ?
The integral of (x^2(ln(x))^2) is 1/3 x^3ln^2(x)-2/3 (1/3 x^3ln(x)-(x^3)/9)+C