What is the integral of x^2ln(9x) ?

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

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integral of x^2ln(9x)

\int x^{2} ln (9 x) d x

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

Solution steps

\int x^{2} ln (9 x) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} ln (9 x) - \int \frac{x ^{2}}{3} d x

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

Add a constant to the solution

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

\frac{d}{d x} (\frac{tan ^{2} ( x )}{tan ( x ^{2} )})

x \frac{d y}{d x} = e^{7 y + x}

n = 1 \sum \infty 5 (- \frac{1}{6})^{5 n}

f (x) = \frac{2 x ^{2} - x - 1}{2 x + 2}

x \to 0 + lim (x^{20 x})

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