What is the integral of (11)/((x-3)(x+8)) ?

The integral of (11)/((x-3)(x+8)) is ln|x-3|-ln|x+8|+C

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integral of (11)/((x-3)(x+8))

\int \frac{11}{( x - 3 ) ( x + 8 )} d x

ln ∣ x - 3 ∣ - ln ∣ x + 8 ∣ + C

Solution steps

\int \frac{11}{( x - 3 ) ( x + 8 )} d x

Take the constant out:

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

= 11 \cdot \int \frac{1}{( x - 3 ) ( x + 8 )} d x

Take the partial fraction of

\frac{1}{( x - 3 ) ( x + 8 )} : \frac{1}{11 ( x - 3 )} - \frac{1}{11 ( x + 8 )}

= 11 \cdot \int \frac{1}{11 ( x - 3 )} - \frac{1}{11 ( x + 8 )} 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

= 11 (\int \frac{1}{11 ( x - 3 )} d x - \int \frac{1}{11 ( x + 8 )} d x)

\int \frac{1}{11 ( x - 3 )} d x = \frac{1}{11} ln ∣ x - 3 ∣

\int \frac{1}{11 ( x + 8 )} d x = \frac{1}{11} ln ∣ x + 8 ∣

= 11 (\frac{1}{11} ln ∣ x - 3 ∣ - \frac{1}{11} ln ∣ x + 8 ∣)

Simplify

11 (\frac{1}{11} ln ∣ x - 3 ∣ - \frac{1}{11} ln ∣ x + 8 ∣) : ln ∣ x - 3 ∣ - ln ∣ x + 8 ∣

= ln ∣ x - 3 ∣ - ln ∣ x + 8 ∣

Add a constant to the solution

= ln ∣ x - 3 ∣ - ln ∣ x + 8 ∣ + C

\int 7 y d y

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\int \frac{x - 3}{3 - 2 x - x ^{2}} d x

\int x^{3} (1 - x^{2})^{- \frac{1}{2}} d x

What is the integral of (11)/((x-3)(x+8)) ?
The integral of (11)/((x-3)(x+8)) is ln|x-3|-ln|x+8|+C