Analysis of Trig and Hyperbolic Substitutions

Trigonometric substitutions are applied to integrate some irrational functions. Because of the similarity of trig and hyperbolic identities, one can apply hyperbolic identities too. But two thing must be kept in mind: 1. Transformed integrand is simple enough to integrate easily, and 2. Domain of integrand must be a subset of the range of the substitution function. All hyperbolic functions do not pass this test. This GeoGebra applet may be used to analyze this fact. Slider may be used to increase or decrease the size of integrand (irrational) functions. Select Trig or Hyperbolic to check on the category of substitutions. The applet helps check the desired substitution. Simultaneously, check the simplicity of the transformed integrand using appropriate identity. For more on hyperbolic functions check my online book "Flipped Classroom Calculus of Single Variable"