Integral of a Quadratic with Distinct Real Roots

Integral of a Quadratic with Distinct Real Roots

If:

$$ax^2+bx+c=a(x-r_1)(x-r_2)$$

where:

$$r_1\neq r_2$$

then:

$$\int\frac{dx}{ax^2+bx+c}=\frac{1}{a(r_1-r_2)}\ln\left|\frac{x-r_1}{x-r_2}\right|+C$$

Usage

- Used after factoring a quadratic denominator into distinct linear factors.