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

y (X) = \frac{5 X ^{3} + 2 X ^{2} - 1}{X ^{2}}

x \to \infty lim (\frac{x}{x})

\int e^{t} d t

\frac{d}{d x} ((1 + x)^{5})

\int \frac{tan ^{2} ( 3 x )}{csc ( 3 x )} d x

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