Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In integral calculus, the Weierstrass substitution, named after Karl Weierstrass, is used for finding antiderivatives, and hence definite integrals, of rational functions of trigonometric functions. No generality is lost by taking these to be rational functions of the sine and cosi ...Full description
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In integral calculus, the Weierstrass substitution, named after Karl Weierstrass, is used for finding antiderivatives, and hence definite integrals, of rational functions of trigonometric functions. No generality is lost by taking these to be rational functions of the sine and cosine. The substitution involves tangents of half-angles. Michael Spivak wrote that "The world's sneakiest substitution is undoubtedly" this technique.