integral of (ax)/(x^2-px)

解答

\int \frac{a x}{x ^{2} - p x} d x

a ln ∣ x - p ∣ + C

求解步骤

\int \frac{a x}{x ^{2} - p x} d x

提出常数:

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

= a \cdot \int \frac{x}{x ^{2} - p x} d x

化简

\frac{x}{x ^{2} - p x} : \frac{1}{x - p}

= a \cdot \int \frac{1}{x - p} d x

使用换元积分法

= a \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= a ln ∣ u ∣

u = x - p

代回

= a ln ∣ x - p ∣

解答补常数

= a ln ∣ x - p ∣ + C

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