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?