integral from 1 to 2 of x^6ln(x)

解答

\int_{1}^{2} x^{6} ln (x) d x

- \frac{127}{49} + \frac{128}{7} ln (2)

十进制

10.08285 \dots

求解步骤

\int_{1}^{2} x^{6} ln (x) d x

使用分布积分法

= [\frac{1}{7} x^{7} ln (x) - \int \frac{x ^{6}}{7} d x]_{1}^{2}

\int \frac{x ^{6}}{7} d x = \frac{x ^{7}}{49}

= [\frac{1}{7} x^{7} ln (x) - \frac{x ^{7}}{49}]_{1}^{2}

带入上下限计算后得:

- \frac{127}{49} + \frac{128}{7} ln (2)

= - \frac{127}{49} + \frac{128}{7} ln (2)

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