integral of x^{11}ln(9x^6)

解答

\int x^{11} ln (9 x^{6}) d x

\frac{1}{6} x^{12} (ln (3) + 3 ln (x)) - \frac{x ^{12}}{24} + C

求解步骤

\int x^{11} ln (9 x^{6}) d x

使用分布积分法

= \frac{1}{12} x^{12} ln (9 x^{6}) - \int \frac{x ^{11}}{2} d x

\int \frac{x ^{11}}{2} d x = \frac{x ^{12}}{24}

= \frac{1}{12} x^{12} ln (9 x^{6}) - \frac{x ^{12}}{24}

\frac{1}{12} x^{12} ln (9 x^{6}) = \frac{1}{6} x^{12} (ln (3) + 3 ln (x))

= \frac{1}{6} x^{12} (ln (3) + 3 ln (x)) - \frac{x ^{12}}{24}

解答补常数

= \frac{1}{6} x^{12} (ln (3) + 3 ln (x)) - \frac{x ^{12}}{24} + C

\int (\frac{x ^{4} - 1}{x})^{2} d x

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