- #1
PFuser1232
- 479
- 20
I am familiar with both trigonometric (circular) and hyperbolic substitutions, and I have solved several integrals using both substitutions.
I feel like trigonometric substitutions are a lot simpler, however. Even in cases where the substitution yields an integral of secant raised to an odd power. I feel like it's a lot easier to apply the reduction formula for secant than to memorize and apply hyperbolic identities.
Granted, hyperbolic identities are not that different from circular identities, but oftentimes I forget the logarithmic form of inverse hyperbolic functions.
So what my question boils down to is:
Are there any cases where trigonometric substitution fails?
I feel like trigonometric substitutions are a lot simpler, however. Even in cases where the substitution yields an integral of secant raised to an odd power. I feel like it's a lot easier to apply the reduction formula for secant than to memorize and apply hyperbolic identities.
Granted, hyperbolic identities are not that different from circular identities, but oftentimes I forget the logarithmic form of inverse hyperbolic functions.
So what my question boils down to is:
Are there any cases where trigonometric substitution fails?