I am familiar with both trigonometric (circular) and hyperbolic substitutions, and I have solved several integrals using both substitutions.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Are hyperbolic substitutions absolutely necessary?

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