The Weierstrass substitution, also called the tangent half-angle 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 undoubtedly 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).
See also
Gröbner Basis,
Half-Angle Formulas,
Hyperbolic Substitution,
Trigonometric Substitution
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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. https://www.mathematicaguidebooks.org/.Referenced
on Wolfram|Alpha
Weierstrass Substitution
Cite this as:
Weisstein, Eric W. "Weierstrass Substitution."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/WeierstrassSubstitution.html
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