What is the integral from 1 to 10 of xln(x) ?

The integral from 1 to 10 of xln(x) is 50ln(10)-99/4

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integral from 1 to 10 of xln(x)

\int_{1}^{10} x ln (x) d x

50 ln (10) - \frac{99}{4}

Decimal Notation

90.37925 \dots

Solution steps

\int_{1}^{10} x ln (x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{10}

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{10}

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{10}

Compute the boundaries:

50 ln (10) - \frac{99}{4}

= 50 ln (10) - \frac{99}{4}

x \to \infty lim (3 x - 9 x^{2} + x)

\int \frac{3 x - 1}{x ^{2} + 10 x + 28} d x

x^{2} sin^{6} (x) + x cos^{- 3} (x)

\frac{d}{d x} (\frac{e ^{2 x}}{e ^{2 x} + 1})

\frac{d}{d y} (\frac{y}{y + \frac{c}{y}})

What is the integral from 1 to 10 of xln(x) ?
The integral from 1 to 10 of xln(x) is 50ln(10)-99/4