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

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

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integral of x^2*ln^2(x)

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

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

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

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

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

Add a constant to the solution

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

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

\frac{7}{x}

\frac{d}{d x} (cosh (cos (x)))

x \to 0 lim (\frac{sin ( 2 x )}{arcsin ( x )})

\frac{d}{d x} ((x^{2} + 5)^{7})

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