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 Discriminant. If , then
|
(5) |
Now use Partial Fraction Decomposition,
|
(6) |
|
(7) |
so
and
. Plugging these in,
for . Note that this integral is also tabulated in Gradshteyn and Ryzhik (1979, 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, 5th ed. San Diego, CA:
Academic Press, 1979.
© 1996-9 Eric W. Weisstein
1999-05-25