integral from 2 to \sqrt[3]{3 of} 1/x

解答

\int_{2}^{33} \frac{1}{x} d x

- ln (2) + \frac{1}{3} ln (3)

十进制

- 0.32694 \dots

求解步骤

\int_{2}^{33} \frac{1}{x} d x

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{33}^{2} \frac{1}{x} d x

使用积分常见定则:

\int \frac{1}{x} d x = ln (∣ x ∣)

= - [ln ∣ x ∣]_{33}^{2}

带入上下限计算后得:

ln (2) - \frac{1}{3} ln (3)

= - (ln (2) - \frac{1}{3} ln (3))

化简

= - ln (2) + \frac{1}{3} ln (3)

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