integral from 5 to 20 of 5/(x+8)

解答

\int_{5}^{20} \frac{5}{x + 8} d x

5 (ln (28) - ln (13))

十进制

3.83627 \dots

求解步骤

\int_{5}^{20} \frac{5}{x + 8} d x

提出常数:

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

= 5 \cdot \int_{5}^{20} \frac{1}{x + 8} d x

使用换元积分法

= 5 \cdot \int_{13}^{28} \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 [ln ∣ u ∣]_{13}^{28}

带入上下限计算后得:

ln (28) - ln (13)

= 5 (ln (28) - ln (13))

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