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

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

\int (x^{2} \cdot 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

\frac{1}{t ^{4}}

\int (sin (y) - y sin (x)) d x

\frac{\partial}{\partial t} (x + y sin (t))

\frac{d}{d x} (x^{2} + c^{2})

\frac{d}{d x} (\frac{2}{2 + 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