integral from 1 to 6 of x^4ln(x)

解答

\int_{1}^{6} x^{4} ln (x) d x

- 311 + \frac{7776}{5} ln (6)

十进制

2475.54432 \dots

求解步骤

\int_{1}^{6} x^{4} ln (x) d x

使用分布积分法

= [\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x]_{1}^{6}

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= [\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}]_{1}^{6}

带入上下限计算后得:

- 311 + \frac{7776}{5} ln (6)

= - 311 + \frac{7776}{5} ln (6)

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