Weierstrass Substitution

The Weierstrass substitution is the trigonometric substitution  which transforms an integral of the form

into one of the form

According to Spivak (2006, pp. 382-383), this is undoubtable the world's sneakiest substitution.

The Weierstrass substitution can also be useful in computing a Gröbner basis to eliminate trigonometric functions from a system of equations (Trott 2006, p. 39).

REFERENCES:

Anton, H. Calculus: A New Horizon, 6th ed. New York: Wiley, pp. 518-519, 1999.

Spivak, M. Calculus, 3rd ed. Cambridge, England: Cambridge University Press, 2006.

Stewart, J. Calculus: Early Transcendentals, 2d ed. Brooks/Cole, p. 439, 1991.

Trott, M. The Mathematica GuideBook for Symbolics. New York: Springer-Verlag, 2006. http://www.mathematicaguidebooks.org/.