What is the integral of 2/3 x^2ln(x) ?

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

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integral of 2/3 x^2ln(x)

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

\frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{2}{3} \cdot \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{2}{3} (\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{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9})

Add a constant to the solution

= \frac{2}{3} (\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}) + C

x \to 1 lim (\frac{( x ^{2} - 5 )}{x})

x \to 5 lim (8 x + 5)

\frac{d}{d x} (e^{x^{2} y} - 2 x - 2 y)

\int x^{3} e^{12 x} d x

\frac{d}{d x} ((x^{4} + 3 x)^{- 1})

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