integral of x^{13}ln(8x^7)

解答

\int x^{13} ln (8 x^{7}) d x

\frac{1}{14} x^{14} (3 ln (2) + 7 ln (x)) - \frac{x ^{14}}{28} + C

求解步骤

\int x^{13} ln (8 x^{7}) d x

使用分布积分法

= \frac{1}{14} x^{14} ln (8 x^{7}) - \int \frac{x ^{13}}{2} d x

\int \frac{x ^{13}}{2} d x = \frac{x ^{14}}{28}

= \frac{1}{14} x^{14} ln (8 x^{7}) - \frac{x ^{14}}{28}

\frac{1}{14} x^{14} ln (8 x^{7}) = \frac{1}{14} x^{14} (3 ln (2) + 7 ln (x))

= \frac{1}{14} x^{14} (3 ln (2) + 7 ln (x)) - \frac{x ^{14}}{28}

解答补常数

= \frac{1}{14} x^{14} (3 ln (2) + 7 ln (x)) - \frac{x ^{14}}{28} + C

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