“Quadratic Integral”的概念、定义、习题解题方法及翻译-数学辞典

单词

Quadratic Integral

释义

Quadratic Integral

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)

and

. Plugging these in,

for

. Note that this integral is also tabulated in Gradshteyn and Ryzhik (1979, equation 2.172), where it is givenwith 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.

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