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

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

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integral of x^2*ln(x^2)

\int x^{2} \cdot ln (x^{2}) d x

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

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} x^{3} ln (x^{2}) - \int \frac{2 x ^{2}}{3} d x

= \frac{1}{3} x^{3} ln (x^{2}) - \int \frac{2 x ^{2}}{3} d x

\int \frac{2 x ^{2}}{3} d x = \frac{2 x ^{3}}{9}

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

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

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

Add a constant to the solution

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

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