Assume that the discriminant q = b2 − 4ac is positive. In that case, define u and A by
The quadratic integral can now be written as
allows us to evaluate the integral:
The final result for the original integral, under the assumption that q > 0, is
- This (hastily written) section may need attention.
In case the discriminant q = b2 − 4ac is negative, the second term in the denominator in
is positive. Then the integral becomes
- Weisstein, Eric W. "Quadratic Integral." From MathWorld--A Wolfram Web Resource, wherein the following is referenced:
- Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, 2000.