Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Cauchy-Schlomilch transformation   The Cauchy-Schl\"omilch transformation states that for a function $f$ and $a,
\, b > 0$, the integral of $f(x^{2})$ and $af((ax-bx^{-1})^{2}$ over the
interval $[0, \infty)$ are the same. This elementary result is used to evaluate
many non-elementary definite integrals, most of which cannot be obtained by
symbolic packages. Applications to probability distributions is also given.

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The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ