What is the integral of (2x-10)/(x^2-10x+106) ?

The integral of (2x-10)/(x^2-10x+106) is ln|x^2-10x+106|+C

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integral of (2x-10)/(x^2-10x+106)

\int \frac{2 x - 10}{x ^{2} - 10 x + 106} d x

ln x^{2} - 10 x + 106 + C

Solution steps

\int \frac{2 x - 10}{x ^{2} - 10 x + 106} d x

Apply u-substitution

= \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{2} - 10 x + 106

= ln x^{2} - 10 x + 106

Add a constant to the solution

= ln x^{2} - 10 x + 106 + C

What is the integral of (2x-10)/(x^2-10x+106) ?
The integral of (2x-10)/(x^2-10x+106) is ln|x^2-10x+106|+C