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

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

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integral of x^2*ln(2x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

Add a constant to the solution

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

x \to 2 lim (\frac{3 x - 2}{x - 8})

\int_{0}^{1} \frac{1}{x ^{\frac{19}{18}}} d x

\frac{d}{d x} (e^{x^{2}} + x^{2})

\int \frac{1}{- x ^{2} - 10 x} d x

y = ln (7 x^{2} + 9 y^{2})

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