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

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

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integral of ln(x)(x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

Add a constant to the solution

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

\int sec (2 θ) d θ

f (x) = 4 x^{2} - 2 x + 5

(sec^{2} (x))^{^{'}}

\int (- 4 x^{3}) d x

x \to 0 + lim (tan^{x} (9 x))

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