integral from 0 to a of x/(a^2-x^2)

解答

\int_{0}^{a} \frac{x}{a ^{2} - x ^{2}} d x

发散

求解步骤

\int_{0}^{a} \frac{x}{a ^{2} - x ^{2}} d x

使用换元积分法

: \int_{a^{2}}^{0} - \frac{1}{2 u} d u

= \int_{a^{2}}^{0} - \frac{1}{2 u} d u

提出常数:

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

= - \frac{1}{2} \cdot \int_{a^{2}}^{0} \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{2} [ln ∣ u ∣]_{a^{2}}^{0}

带入上下限计算后得:

发散

= 发散

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