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

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

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integral of x^2ln(3x)

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

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

Solution steps

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

Apply Integration By Parts

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

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

Add a constant to the solution

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

\int_{0}^{v} v d v

\int - 32 t + 18 d t

\int_{0}^{3} \frac{1}{x x} d x

x \to 0 lim (- sin (x) + x)

f (x) = x (8 - x)^{3}

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