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

\frac{d}{d x} (x^{4} - 5 x^{3})

\frac{d}{d x} (\frac{x + 10}{x - 10})

\int x 1 + x d x

ln (8 x + 5)

x y^{^{'}} + 9 y = 12 y^{2}, y (1) = - 1

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