Are there any integrals that can't be solved with only trig substitution? An integral that requires you to use a hyperbolic or inverse hyperbolic substitution?
2026-03-29 17:13:19.1774804399
Are there integrals you can't solve without inverse hyperbolic substitution?
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One way of viewing the hyperbolic functions is that they are "abbreviations" for combinations of exponential functions, so whatever can be done using hyperbolic functions can equally be done using exponentials - albeit in a less concise manner. Similarly, inverse hyperbolics are really just log functions in various combinations.
What this means is that if an integral can be done with a hyperbolic substitution, then it can also be done without hyperbolics, by means of a (possibly more complicated) substitution involving exponential functions.