What is the integral from 1 to 4 of xln(x) ?

The integral from 1 to 4 of xln(x) is 16ln(2)-15/4

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integral from 1 to 4 of xln(x)

\int_{1}^{4} x ln (x) d x

16 ln (2) - \frac{15}{4}

Decimal

7.34035 \dots

Solution steps

\int_{1}^{4} x ln (x) d x

Apply Integration By Parts

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

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

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

Compute the boundaries:

16 ln (2) - \frac{15}{4}

= 16 ln (2) - \frac{15}{4}

What is the integral from 1 to 4 of xln(x) ?
The integral from 1 to 4 of xln(x) is 16ln(2)-15/4