What is the integral of-1/(x+8)+9/(x-4) ?

The integral of-1/(x+8)+9/(x-4) is -ln|x+8|+9ln|x-4|+C

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integral of-1/(x+8)+9/(x-4)

\int - \frac{1}{x + 8} + \frac{9}{x - 4} d x

- ln ∣ x + 8 ∣ + 9 ln ∣ x - 4 ∣ + C

Solution steps

\int - \frac{1}{x + 8} + \frac{9}{x - 4} 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{1}{x + 8} d x + \int \frac{9}{x - 4} d x

\int \frac{1}{x + 8} d x = ln ∣ x + 8 ∣

\int \frac{9}{x - 4} d x = 9 ln ∣ x - 4 ∣

= - ln ∣ x + 8 ∣ + 9 ln ∣ x - 4 ∣

Add a constant to the solution

= - ln ∣ x + 8 ∣ + 9 ln ∣ x - 4 ∣ + C

f (x) = - \frac{1}{x ^{2}}

\frac{d}{d x} (x^{- 5 c o s (x)})

x \to 1 lim (4 x^{2} + 2 x + 5)

\frac{d}{d x} (- 3 ln (x))

\int t sin (\frac{t}{2}) d t

What is the integral of-1/(x+8)+9/(x-4) ?
The integral of-1/(x+8)+9/(x-4) is -ln|x+8|+9ln|x-4|+C