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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

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

Add a constant to the solution

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

(e^{- y})^{^{'}}

x \frac{d y}{d x} + x y^{2} = x y

\int \frac{x - 1}{4 x ^{3} + 4 x ^{2} + x} d x

\int sin^{2} (2 x + 5) d x

\frac{\partial}{\partial x} (e^{- 7 y} cos (7 x))

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