What is the integral of x^2ln(6x) ?

The integral of x^2ln(6x) is 1/3 x^3ln(6x)-(x^3)/9+C

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integral of x^2ln(6x)

\int x^{2} ln (6 x) d x

\frac{1}{3} x^{3} ln (6 x) - \frac{x ^{3}}{9} + C

Solution steps

\int x^{2} ln (6 x) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} ln (6 x) - \int \frac{x ^{2}}{3} d x

= \frac{1}{3} x^{3} ln (6 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 (6 x) - \frac{x ^{3}}{9}

Add a constant to the solution

= \frac{1}{3} x^{3} ln (6 x) - \frac{x ^{3}}{9} + C

\int 3 x^{2} + 4 x - 1 d x

\frac{d}{d x} (x y)

(4 x + y e^{\frac{y}{x}}) d x - x e^{\frac{y}{x}} d y = 0

(e^{- x}) (x^{2} - x)

What is the integral of x^2ln(6x) ?
The integral of x^2ln(6x) is 1/3 x^3ln(6x)-(x^3)/9+C