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Date: 28-8-2018
1975
Date: 26-7-2019
1555
Date: 11-6-2019
1112
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To compute an integral of the form
(1) |
complete the square in the denominator to obtain
(2) |
Let . Then define
(3) |
where
(4) |
is the negative of the polynomial discriminant. If , then
(5) |
Now use partial fraction decomposition,
(6) |
(7) |
so and . Plugging these in,
(8) |
for . Note that this integral is also tabulated in Gradshteyn and Ryzhik (2000, equation 2.172), where it is given with a sign flipped.
REFERENCES:
Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, 2000.
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