integral from 0 to 5 of xln(x)

解答

\int_{0}^{5} x ln (x) d x

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

十进制

13.86797 \dots

求解步骤

\int_{0}^{5} x ln (x) d x

使用分布积分法

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{5}

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{0}^{5}

带入上下限计算后得:

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

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

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