What is the integral from 3 to 5 of xln(x) ?

The integral from 3 to 5 of xln(x) is -4+(25ln(5)-9ln(3))/2

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integral from 3 to 5 of xln(x)

\int_{3}^{5} x ln (x) d x

- 4 + \frac{25 ln ( 5 ) - 9 ln ( 3 )}{2}

Decimal

11.17421 \dots

Solution steps

\int_{3}^{5} x ln (x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{3}^{5}

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{3}^{5}

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{3}^{5}

Compute the boundaries:

- 4 + \frac{25 ln ( 5 ) - 9 ln ( 3 )}{2}

= - 4 + \frac{25 ln ( 5 ) - 9 ln ( 3 )}{2}

\int_{2}^{6} 2 x^{2} - 16 x + 24 d x

\int_{0}^{5} \frac{1}{x} d x

\int_{\frac{π}{4}}^{\frac{3 π}{4}} cot (x) d x

\int_{π}^{2 π} 5 sin (2 x) d x

\int_{0}^{4} 3 x d x

What is the integral from 3 to 5 of xln(x) ?
The integral from 3 to 5 of xln(x) is -4+(25ln(5)-9ln(3))/2