What is the integral of 1/(x^2-12x+35) ?

The integral of 1/(x^2-12x+35) is -1/2 ln|x-5|+1/2 ln|x-7|+C

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integral of 1/(x^2-12x+35)

\int \frac{1}{x ^{2} - 12 x + 35} d x

- \frac{1}{2} ln ∣ x - 5 ∣ + \frac{1}{2} ln ∣ x - 7 ∣ + C

Solution steps

\int \frac{1}{x ^{2} - 12 x + 35} d x

Take the partial fraction of

\frac{1}{x ^{2} - 12 x + 35} : - \frac{1}{2 ( x - 5 )} + \frac{1}{2 ( x - 7 )}

= \int - \frac{1}{2 ( x - 5 )} + \frac{1}{2 ( x - 7 )} 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}{2 ( x - 5 )} d x + \int \frac{1}{2 ( x - 7 )} d x

\int \frac{1}{2 ( x - 5 )} d x = \frac{1}{2} ln ∣ x - 5 ∣

\int \frac{1}{2 ( x - 7 )} d x = \frac{1}{2} ln ∣ x - 7 ∣

= - \frac{1}{2} ln ∣ x - 5 ∣ + \frac{1}{2} ln ∣ x - 7 ∣

Add a constant to the solution

= - \frac{1}{2} ln ∣ x - 5 ∣ + \frac{1}{2} ln ∣ x - 7 ∣ + C

3 x^{^{'}} - 5 x = 12

\frac{d y}{d x} = \frac{1}{2} x + y - 1

y^{^{''''}} + 18 y^{^{''}} + 81 y = 0

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

\frac{d}{d x} (\frac{2 x}{( 1 + x ) ^{2}})

What is the integral of 1/(x^2-12x+35) ?
The integral of 1/(x^2-12x+35) is -1/2 ln|x-5|+1/2 ln|x-7|+C