What is the integral from 0 to 2 of x^2ln(x) ?

The integral from 0 to 2 of x^2ln(x) is 8/3 ln(2)-8/9

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integral from 0 to 2 of x^2ln(x)

\int_{0}^{2} x^{2} ln (x) d x

\frac{8}{3} ln (2) - \frac{8}{9}

Solution steps

\int_{0}^{2} x^{2} ln (x) d x

Apply Integration By Parts

: [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{0}^{2}

= [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{0}^{2}

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{0}^{2}

Compute the boundaries:

\frac{8}{3} ln (2) - \frac{8}{9}

= \frac{8}{3} ln (2) - \frac{8}{9}

f (x) = x^{3} + 1, (1, 2)

\int \frac{5 - e ^{- x}}{e ^{- x}} d x

\int \frac{x ^{2}}{x - 3} d x

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\frac{d}{d x} (e^{s i n (x - 1)})

What is the integral from 0 to 2 of x^2ln(x) ?
The integral from 0 to 2 of x^2ln(x) is 8/3 ln(2)-8/9