I'm going to be picky for a second. Pop open any Calculus book and you'll find a table of integrals:

Stewart 7th Edition Single Variable Calculus

Stewart 7th Edition Single Variable Calculus

For whatever reason, the natural base is always called out as unique and special. If you look at the equivalent derivative table you'll see it gets a call out from a generic exponential. But why do this? The natural base e is just a number, albeit irrational. If you integrate a base e exponential using the generic rule, you get e^x / ln e which reduces to e^x.

Calling it out as something special with a different rule loses site of base e being one of many possible bases for exponential functions. That somehow e isn't just a number. The same hang up exists with π whether you've noticed it or not. And it furthers the love of special cases: specific steps must be remembered for almost everything, when really you've missed an opportunity to show algebra in action.

Posted
AuthorJonathan Claydon