log|x| + C revisited

log|x| + C revisited Posted by Mike Shulman A while ago on this blog, Tom posted a question about teaching calculus: what do you tell students the value of is? The standard answer is , with an “arbitrary constant”. But that’s wrong if means (as we also usually tell students it does) the “most general antiderivative”, since is a more general antiderivative, for two arbitrary constants and . (I’m writing for the natural logarithm function that Tom wrote as , for reasons that will become clear...