What is the integral from 0 to 1 of xln(x) ?

The integral from 0 to 1 of xln(x) is -1/4

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integral from 0 to 1 of xln(x)

\int_{0}^{1} x ln (x) d x

- \frac{1}{4}

Decimal

- 0.25

Solution steps

\int_{0}^{1} x ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- \frac{1}{4}

= - \frac{1}{4}

\int \frac{1}{x ^{2}} 2 + \frac{1}{x} d x

\int \frac{( x ^{- 2} - 4 )}{x ^{3}} d x

\int (2 x - 3)^{2} (2 x - 3)^{2} + 4 d x

cos^{2} (17 t)

x \to \infty lim (\frac{x ^{l n (n)}}{x ^{l n (n) + 1}})

What is the integral from 0 to 1 of xln(x) ?
The integral from 0 to 1 of xln(x) is -1/4