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受欢迎的微积分 >

integral of (21)/(0.07x+5)

解答

\int \frac{21}{0.07 x + 5} d x

解答

300 ln ∣ 0.07 x + 5 ∣ + C

求解步骤

\int \frac{21}{0.07 x + 5} d x

提出常数:

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

= 21 \cdot \int \frac{1}{0.07 x + 5} d x

使用换元积分法

= 21 \cdot \int \frac{1}{0.07 u} d u

提出常数:

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

= 21 \cdot \frac{1}{0.07} \cdot \int \frac{1}{u} d u

化简

= 21 \cdot 14.28571 \dots \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 21 \cdot 14.28571 \dots ln ∣ u ∣

u = 0.07 x + 5

代回

= 21 \cdot 14.28571 \dots ln ∣ 0.07 x + 5 ∣

化简

= 300 ln ∣ 0.07 x + 5 ∣

解答补常数

= 300 ln ∣ 0.07 x + 5 ∣ + C

作图

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