integral of 8xln(7x)

解答

\int 8 x ln (7 x) d x

8 (\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}) + C

求解步骤

\int 8 x ln (7 x) d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 8 \cdot \int x ln (7 x) d x

使用分布积分法

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= 8 (\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4})

解答补常数

= 8 (\frac{1}{2} x^{2} ln (7 x) - \frac{x ^{2}}{4}) + C

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