integral from e^3 to e^5 of 1/(xln(x))

解答

\int_{e^{3}}^{e^{5}} \frac{1}{x ln ( x )} d x

ln (5) - ln (3)

十进制表示法

0.51082 \dots

求解步骤

\int_{e^{3}}^{e^{5}} \frac{1}{x ln ( x )} d x

使用换元积分法

: \int_{3}^{5} \frac{1}{u} d u

= \int_{3}^{5} \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{3}^{5}

带入上下限计算后得:

ln (5) - ln (3)

= ln (5) - ln (3)

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