integral from 5 to 8 of (30)/x

解答

\int_{5}^{8} \frac{30}{x} d x

30 (3 ln (2) - ln (5))

十进制

14.10010 \dots

求解步骤

\int_{5}^{8} \frac{30}{x} d x

提出常数:

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

= 30 \cdot \int_{5}^{8} \frac{1}{x} d x

使用积分常见定则:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 30 [ln ∣ x ∣]_{5}^{8}

带入上下限计算后得:

3 ln (2) - ln (5)

= 30 (3 ln (2) - ln (5))

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