What is the integral of 1/((x-4)(x+3)) ?

The integral of 1/((x-4)(x+3)) is 1/7 ln|x-4|-1/7 ln|x+3|+C

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integral of 1/((x-4)(x+3))

\int \frac{1}{( x - 4 ) ( x + 3 )} d x

\frac{1}{7} ln ∣ x - 4 ∣ - \frac{1}{7} ln ∣ x + 3 ∣ + C

Solution steps

\int \frac{1}{( x - 4 ) ( x + 3 )} d x

Take the partial fraction of

\frac{1}{( x - 4 ) ( x + 3 )} : \frac{1}{7 ( x - 4 )} - \frac{1}{7 ( x + 3 )}

= \int \frac{1}{7 ( x - 4 )} - \frac{1}{7 ( x + 3 )} 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}{7 ( x - 4 )} d x - \int \frac{1}{7 ( x + 3 )} d x

\int \frac{1}{7 ( x - 4 )} d x = \frac{1}{7} ln ∣ x - 4 ∣

\int \frac{1}{7 ( x + 3 )} d x = \frac{1}{7} ln ∣ x + 3 ∣

= \frac{1}{7} ln ∣ x - 4 ∣ - \frac{1}{7} ln ∣ x + 3 ∣

Add a constant to the solution

= \frac{1}{7} ln ∣ x - 4 ∣ - \frac{1}{7} ln ∣ x + 3 ∣ + C

(x^{2} - 9 x + 9) 25 - x^{2}

x \to 0 lim (\frac{( 3 ^{x} - 2 ^{x} )}{x})

\int (e^{2 x} + e^{- 3 x}) d x

(ln (x))^{5}

\int \frac{x - 2 x ^{2} + 1}{x} d x

What is the integral of 1/((x-4)(x+3)) ?
The integral of 1/((x-4)(x+3)) is 1/7 ln|x-4|-1/7 ln|x+3|+C