integral of-2/(1+x)

解答

\int - \frac{2}{1 + x} d x

- 2 ln ∣ 1 + x ∣ + C

求解步骤

\int - \frac{2}{1 + x} d x

提出常数:

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

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

使用换元积分法

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

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 2 ln ∣ u ∣

u = 1 + x

代回

= - 2 ln ∣ 1 + x ∣

解答补常数

= - 2 ln ∣ 1 + x ∣ + C

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