What is the integral from 2 to 5 of xln(x) ?

The integral from 2 to 5 of xln(x) is -2ln(2)-21/4+25/2 ln(5)

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integral from 2 to 5 of xln(x)

\int_{2}^{5} x ln (x) d x

- 2 ln (2) - \frac{21}{4} + \frac{25}{2} ln (5)

Decimal

13.48167 \dots

Solution steps

\int_{2}^{5} x ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- 2 ln (2) - \frac{21}{4} + \frac{25}{2} ln (5)

= - 2 ln (2) - \frac{21}{4} + \frac{25}{2} ln (5)

\int_{0}^{1} x^{2} y e^{x y} d x

\int_{1}^{2} π (2 - \frac{x}{2})^{2} d x

\int_{0}^{1} (2 x^{4} - 5 x^{2} + 5) d x

\int_{0}^{1} \frac{2}{( 5 + 3 x ) ^{\frac{1}{2}}} d x

\int_{- 4}^{4} - x^{2} + 16 d x

What is the integral from 2 to 5 of xln(x) ?
The integral from 2 to 5 of xln(x) is -2ln(2)-21/4+25/2 ln(5)