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} (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{d}{1} (y))^{2} d x

\frac{( 4 s - 5 )}{s ^{2} - 6 s + 13}

n = 1 \sum \infty (\frac{1}{3})^{n}

4 x^{2}, \frac{x}{4}

y = x^{2} + 4, y = - x^{2} - 1, x = - 2, x = 3

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