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

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

Popular >

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

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

\frac{2 e ^{3}}{9}

Decimal Notation

4.46345 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

3 \cdot \frac{x ^{3}}{9} = \frac{x ^{3}}{3}

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

Compute the boundaries:

\frac{2 e ^{3}}{9}

= \frac{2 e ^{3}}{9}

\frac{d}{d x} (ln (x + e^{x}))

y^{^{'}} = \frac{( 1 - y ) ^{5}}{4}

y = 2 x e^{- x} + 2 e^{x^{5}}

\int x^{5} - sec (x) + \frac{1}{2 x} d x

\int x I n^{2} x d x

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