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.
© 19969 Eric W. Weisstein
19990525