What is the integral from 0 to e of xln(x) ?

The integral from 0 to e of xln(x) is (e^2)/4

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integral from 0 to e of xln(x)

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

\frac{e ^{2}}{4}

Decimal Notation

1.84726 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= [\frac{1}{2} (x^{2} ln (x) - 2 \cdot \frac{x ^{2}}{4})]_{0}^{e}

2 \cdot \frac{x ^{2}}{4} = \frac{x ^{2}}{2}

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

Compute the boundaries:

\frac{e ^{2}}{4}

= \frac{e ^{2}}{4}

y^{^{'}} = (x - 2) (y - 2)

f (x) = - x + 5 x^{- \frac{1}{2}} - 3, (1, 1)

\frac{d y}{d x} = \frac{( x - 3 )}{y - 3}

\int_{0}^{\infty} \frac{1}{1 + x} d x

\int 2 cos^{2} (θ) d θ

What is the integral from 0 to e of xln(x) ?
The integral from 0 to e of xln(x) is (e^2)/4