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受欢迎的微积分 >

integral of 4/(6-2x)

解答

\int \frac{4}{6 - 2 x} d x

解答

- 2 ln ∣ 6 - 2 x ∣ + C

求解步骤

\int \frac{4}{6 - 2 x} d x

提出常数:

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

= 4 \cdot \int \frac{1}{6 - 2 x} d x

使用换元积分法

= 4 \cdot \int - \frac{1}{2 u} d u

提出常数:

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

= 4 (- \frac{1}{2} \cdot \int \frac{1}{u} d u)

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 (- \frac{1}{2} ln ∣ u ∣)

u = 6 - 2 x

代回

= 4 (- \frac{1}{2} ln ∣ 6 - 2 x ∣)

化简

4 (- \frac{1}{2} ln ∣ 6 - 2 x ∣) : - 2 ln ∣ 6 - 2 x ∣

= - 2 ln ∣ 6 - 2 x ∣

解答补常数

= - 2 ln ∣ 6 - 2 x ∣ + C

作图

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