Vardi's integral is the beautiful definite integral

			(1)
			(2)
			(3)

(OEIS A115252; Gradshteyn and Ryzhik 1980, p. 532; Bailey et al. 2007, p. 160; Moll 2006), where  is the gamma function.

Other examples similar to these include

			(4)
			(5)

(Vardi 1988; Gradshteyn and Ryzhik 1980, pp. 571-572).

REFERENCES:

Bailey, D. H.; Borwein, J. M.; Calkin, N. J.; Girgensohn, R.; Luke, D. R.; and Moll, V. H. Experimental Mathematics in Action. Wellesley, MA: A K Peters, 2007.

Bierens de Haan, D. Nouvelles Tables d'intégrales définies. Amsterdam, 1867.

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 4th ed. San Diego, CA: Academic Press, 1980.

Moll, V. H. "Some Questions in the Evaluation of Definite Integrals." MAA Short Course, San Antonio, TX. Jan. 2006. http://crd.lbl.gov/~dhbailey/expmath/maa-course/Moll-MAA.pdf.

Sloane, N. J. A. Sequence A115252 in "The On-Line Encyclopedia of Integer Sequences."

Vardi, I. "Integrals, an Introduction to Analytic Number Theory." Amer. Math. Monthly 95, 308-315, 1988.