integral from a to b of (2/x+1)

解答

\int_{a}^{b} (\frac{2}{x} + 1) d x

2 (ln ∣ b ∣ - ln ∣ a ∣) + b - a

求解步骤

\int_{a}^{b} \frac{2}{x} + 1 d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{a}^{b} \frac{2}{x} d x + \int_{a}^{b} 1 d x

\int_{a}^{b} \frac{2}{x} d x = 2 (ln ∣ b ∣ - ln ∣ a ∣)

\int_{a}^{b} 1 d x = b - a

= 2 (ln ∣ b ∣ - ln ∣ a ∣) + b - a

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