integral from 0 to 1 of x^5ln(x)

解答

\int_{0}^{1} x^{5} ln (x) d x

- \frac{1}{36}

十进制

- 0.02777 \dots

求解步骤

\int_{0}^{1} x^{5} ln (x) d x

使用分布积分法

= [\frac{1}{6} x^{6} ln (x) - \int \frac{x ^{5}}{6} d x]_{0}^{1}

\int \frac{x ^{5}}{6} d x = \frac{x ^{6}}{36}

= [\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36}]_{0}^{1}

带入上下限计算后得:

- \frac{1}{36}

= - \frac{1}{36}

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