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

\int \frac{1}{y - 1} d y

h \to 0 lim (\frac{1 0 ^{h} - 1}{h})

\frac{8}{( 8 - x ^{4} ) ^{\frac{3}{2}}}

\frac{d}{d x} (33 arctan (x))

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

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