What is the integral of 1/((x-6)(x-5)) ?

The integral of 1/((x-6)(x-5)) is ln|x-6|-ln|x-5|+C

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integral of 1/((x-6)(x-5))

\int \frac{1}{( x - 6 ) ( x - 5 )} d x

ln ∣ x - 6 ∣ - ln ∣ x - 5 ∣ + C

Solution steps

\int \frac{1}{( x - 6 ) ( x - 5 )} d x

Take the partial fraction of

\frac{1}{( x - 6 ) ( x - 5 )} : \frac{1}{x - 6} - \frac{1}{x - 5}

= \int \frac{1}{x - 6} - \frac{1}{x - 5} 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 - 6} d x - \int \frac{1}{x - 5} d x

\int \frac{1}{x - 6} d x = ln ∣ x - 6 ∣

\int \frac{1}{x - 5} d x = ln ∣ x - 5 ∣

= ln ∣ x - 6 ∣ - ln ∣ x - 5 ∣

Add a constant to the solution

= ln ∣ x - 6 ∣ - ln ∣ x - 5 ∣ + C

\int \frac{2}{1 - 4 x} d x

\int \frac{1}{x} - \frac{5}{x ^{2} + 1} d x

\int \frac{cos ( x )}{1 + tan ( x )} d x

\int (5 - 6 x) d x

\int x^{e} + e^{2 x} + x^{π} + π^{x} + 1 d x

What is the integral of 1/((x-6)(x-5)) ?
The integral of 1/((x-6)(x-5)) is ln|x-6|-ln|x-5|+C