Prologue

Although it is properly useful in the form in which we find it in reference works such as the Chemical Rubber Company's Handbook of Chemistry and Physics, I have long felt a subtle dissatisfaction with the standard Table of Integrals, a sense that something has gone missing. We can certainly use the integrals and their solutions as they appear in those simple lists, but I believe that we gain a clearer understanding of integrals when we see how mathematicians solved them and see some indication of how people apply them. Over the past five or six years I have solved a number of integrals in my own work, going back over them to assure myself that I understand how to apply them correctly. Rather than stash them away with the notes for which I derived them, I have decided to put them together in one notebook and I have entertained the additional thought of occasionally picking an integral from the standard list, resolving it, finding a suitable application to illustrate its use, and then adding it to this collection. I want to see how big this collection grows before poor health or death oblige me to stop adding to it.

I want to note one other unique feature of this Table of Integrals. Like addition and multiplication, integration is a synthetic process: it comprises multiplication and addition together. I want to solve my integrals with those processes only, without reference to the anti-differentiation that mathematicians commonly use to determine the solutions of integrals. I want my integrals to reflect only integration and not its inverse.

So now onward!

2003 Jun 29