integral of (x+9)/(x-9)-(y+21)/(y+39)

解答

\int \frac{x + 9}{x - 9} - \frac{y + 21}{y + 39}

- \frac{21 + y}{39 + y} x + 18 ln ∣ - 9 + x ∣ + x + C

求解步骤

\int \frac{x + 9}{x - 9} - \frac{y + 21}{y + 39} 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 \frac{21 + y}{39 + y} d x + \int \frac{9 + x}{- 9 + x} d x

\int \frac{21 + y}{39 + y} d x = \frac{21 + y}{39 + y} x

\int \frac{9 + x}{- 9 + x} d x = 18 ln ∣ - 9 + x ∣ + x

= - \frac{21 + y}{39 + y} x + 18 ln ∣ - 9 + x ∣ + x

解答补常数

= - \frac{21 + y}{39 + y} x + 18 ln ∣ - 9 + x ∣ + x + C

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