integral from 1 to 9 of 9/x

解答

\int_{1}^{9} \frac{9}{x} d x

18 ln (3)

十进制

19.77502 \dots

求解步骤

\int_{1}^{9} \frac{9}{x} d x

提出常数:

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

= 9 \cdot \int_{1}^{9} \frac{1}{x} d x

使用积分常见定则:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 9 [ln ∣ x ∣]_{1}^{9}

带入上下限计算后得:

2 ln (3)

= 9 \cdot 2 ln (3)

化简

= 18 ln (3)

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