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,
 (8)
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