What is the integral from 1 to 7 of xln(x) ?

The integral from 1 to 7 of xln(x) is -12+49/2 ln(7)

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integral from 1 to 7 of xln(x)

\int_{1}^{7} x ln (x) d x

- 12 + \frac{49}{2} ln (7)

Decimal

35.67479 \dots

Solution steps

\int_{1}^{7} x ln (x) d x

Apply Integration By Parts

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{7}

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{7}

Compute the boundaries:

- 12 + \frac{49}{2} ln (7)

= - 12 + \frac{49}{2} ln (7)

What is the integral from 1 to 7 of xln(x) ?
The integral from 1 to 7 of xln(x) is -12+49/2 ln(7)