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受欢迎的微积分 >

integral of 3/(6x-9)

解答

\int \frac{3}{6 x - 9} d x

解答

\frac{1}{2} ln ∣ 6 x - 9 ∣ + C

求解步骤

\int \frac{3}{6 x - 9} d x

提出常数:

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

= 3 \cdot \int \frac{1}{6 x - 9} d x

使用换元积分法

= 3 \cdot \int \frac{1}{6 u} d u

提出常数:

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

= 3 \cdot \frac{1}{6} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{6} ln ∣ u ∣

u = 6 x - 9

代回

= 3 \cdot \frac{1}{6} ln ∣ 6 x - 9 ∣

化简

3 \cdot \frac{1}{6} ln ∣ 6 x - 9 ∣ : \frac{1}{2} ln ∣ 6 x - 9 ∣

= \frac{1}{2} ln ∣ 6 x - 9 ∣

解答补常数

= \frac{1}{2} ln ∣ 6 x - 9 ∣ + C

作图

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