Dec 20, 2014 · This doesn't seem to answer OP's question, which asks how to determing a trig or hyperbolic trig substitution is more appropriate (presumably when evaluating integrals), not what …

It is hard to visualize the bounds of the substitution that will keep it positive but I think that is something I can just memorize from a table. So this is similar to u substitution except that I am not using a single …

The key issue is that both the trigonometric and the hyperbolic substitutions lead to simpler integrals, because the irrational integrand becomes a rational function of trigonometric or hyperbolic functions.

Trigonometric Substitution - Arc Length Ask Question Asked 12 years, 10 months ago Modified 12 years, 10 months ago

These comments apply to any trigonometric (or other) substitutions that involve choices or an apparent dependence of the post-substitution calculations on the choices.

How to determine limits of integration for trig substitution? Ask Question Asked 9 years, 9 months ago Modified 9 years, 9 months ago

U-substitution is for functions that can be written as the product of another function and its derivative. $$\int u du$$ Integration by parts is for functions that can be written as the product of another …

Sep 27, 2020 · The latter manner is commonly used in trigonometric substitution, replacing the original variable with a trigonometric function of a new variable and the original differential with the differential …

Oct 24, 2021 · From what I've gathered, every text book says we can do trig substitution with either sin, sec or tan. Some other examples use tan (x/2), but so far I've never encountered cosine substitution.

More to what you asked, any x outside the $\pm a$ range is complex, so having a trig substitution function that is "bounded" is totally appropriate. If you're doing complex integration, have bounds …