integral from 1 to 6 of x^3ln(x)

解答

\int_{1}^{6} x^{3} ln (x) d x

324 ln (6) - \frac{1295}{16}

十进制

499.59256 \dots

求解步骤

\int_{1}^{6} x^{3} ln (x) d x

使用分布积分法

= [\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x]_{1}^{6}

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= [\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}]_{1}^{6}

带入上下限计算后得:

324 ln (6) - \frac{1295}{16}

= 324 ln (6) - \frac{1295}{16}

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