What is the integral of x^2ln|x| ?

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

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integral of x^2ln|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

x \to 1 lim (x (x - 1) ln (x + 1))

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

\frac{1}{2} e^{t} - \frac{1}{2} cos (t) - \frac{1}{2} sin (t)

2 e^{2 t}

y = x - 2, x = y^{2}

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