In this video, we discuss the integration technique known as the tangent half-angle substitution, the Weierstrass substitution, or universal trigonometric substitution. This technique can be applied to find integrals for which other techniques might not work. We use it to find the integral of csc(x), which has another technique, and for 1/(1+sin(x)+cos(x)). Can you think of other integrals where this technique might work?

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This animation is based on a visual proof by Sidney H. Kung from the December 2001 issue of Mathematics Magazine (https://www.jstor.org/stable/2691035 - page 393).

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