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受欢迎的微积分 >

integral of 1/(0.15p+20)

解答

\int \frac{1}{0.15 p + 20} d p

解答

6.66666 \dots ln ∣ 0.15 p + 20 ∣ + C

求解步骤

\int \frac{1}{0.15 p + 20} d p

使用换元积分法

= \int \frac{1}{0.15 u} d u

提出常数:

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

= \frac{1}{0.15} \cdot \int \frac{1}{u} d u

化简

= 6.66666 \dots \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 6.66666 \dots ln ∣ u ∣

u = 0.15 p + 20

代回

= 6.66666 \dots ln ∣ 0.15 p + 20 ∣

解答补常数

= 6.66666 \dots ln ∣ 0.15 p + 20 ∣ + C

作图

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