What is the integral of x^2ln(4x) ?

The integral of x^2ln(4x) is 1/3 x^3ln(4x)-(x^3)/9+C

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integral of x^2ln(4x)

\int x^{2} ln (4 x) d x

\frac{1}{3} x^{3} ln (4 x) - \frac{x ^{3}}{9} + C

Solution steps

\int x^{2} ln (4 x) d x

Apply Integration By Parts

: \frac{1}{3} x^{3} ln (4 x) - \int \frac{x ^{2}}{3} d x

= \frac{1}{3} x^{3} ln (4 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 (4 x) - \frac{x ^{3}}{9}

Add a constant to the solution

= \frac{1}{3} x^{3} ln (4 x) - \frac{x ^{3}}{9} + C

x \to - \frac{π}{4} lim (sec (x))

x \to 1 lim (+ (\frac{1}{x ^{2} - 1}))

\int 3 x d x

\int sin^{2} (2 x) cos^{2} (x) d x

x \to 0 lim ((1 - 10 x)^{\frac{1}{x}})

What is the integral of x^2ln(4x) ?
The integral of x^2ln(4x) is 1/3 x^3ln(4x)-(x^3)/9+C