In mathematics, a quadratic integral is an integral of the form
It can be evaluated by completing the square in the denominator.
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
The partial fraction decomposition
The final result for the original integral, under the assumption that q > 0, is
In case the discriminant q = b2 − 4ac is negative, the second term in the denominator in