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

\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

x \frac{d y}{d x} + x y^{2} = x y

\int sin^{2} (2 x + 5) d x

t an g e n t f (x) = 3 x + 7, (3, 4)

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 2 s + 2 )}

e x p an d (x - 2)^{2} (x + 4)

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