What is the integral of (x+9)/(x-9)-(y+21)/(y+39) ?

The integral of (x+9)/(x-9)-(y+21)/(y+39) is -(21+y)/(39+y)x+18ln|-9+x|+x+C

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

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

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

Solution steps

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

Apply the Sum Rule:

\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

Add a constant to the solution

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

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What is the integral of (x+9)/(x-9)-(y+21)/(y+39) ?
The integral of (x+9)/(x-9)-(y+21)/(y+39) is -(21+y)/(39+y)x+18ln|-9+x|+x+C