It’s been so long since I’ve done anything other than the simplest integrals by hand now. Anything that involves numbers, or is more complicated than can be done in a couple of lines, and out comes Maple or Mathematica. However, I’m also often playing with integrals of unknown functions, and using the variational principle on them, and that all has to be done by hand. But that’s ok. Integration by parts is so much more fun when you don’t actually know what the functions are ;).

However, one of the problems in the homework for this week was to do an integral by hand. It wasn’t all that copmlicated, but it has been so long since I’ve done integration by hand, I’ve forgotten most of the tricks that you use. That said, I got it out in good time, but certainly nowhere near as fast as I would have when I was in my prime, about the end of 12th grade. Regardless, I rather enjoyed doing the integral. It was somewhat… aesthetically pleasing đź™‚

I’ve sometimes thought of making a section of my website devoted to explaining how integrals are done, and stepping through some of the more ugly ones, ones that you usually just look up in a book and wonder “how on earth did they arrive at that”. Maybe I’ll get around to doing that sometime. Just maybe.

But for the moment, I’m going to bed đź™‚ Hope all is well, wherever you are!

~Jolyon

Edit: If you were interested in the integral, it was an indefinite integral, which in LaTeX code reads:

\int \frac{\sqrt{\frac{2M}{r}}}{1-\frac{2M}{r}} dr