integral of 1/(A-Bx)

解答

\int \frac{1}{A - B x} d x

- \frac{1}{B} ln ∣ A - B x ∣ + C

求解步骤

\int \frac{1}{A - B x} d x

使用换元积分法

= \int - \frac{1}{B u} d u

提出常数:

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

= - \frac{1}{B} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{B} ln ∣ u ∣

u = A - B x

代回

= - \frac{1}{B} ln ∣ A - B x ∣

解答补常数

= - \frac{1}{B} ln ∣ A - B x ∣ + C