Recent content by PhantomOort

It's for integrals like \int x sin(x) dx, which are usually done by parts. Not that this is super hard, but with the shortcut, \lambda=0, \mu = -1, and the result is sin(x)-xcos(x) and we're done. PS, my apologies to any readers put off by the formatting. I'm utterly unfamiliar with this...

Damn, I could have done that! I need to stop being so lazy. Thanks.

Yes, both \lambda and \mu are numbers. Obviously this only works in cases where they exist, such as for exponentials, trig functions, or x. But these make up a great many common integrals, so it's a pretty good shortcut.

Hi all. I've recently learned a shortcut for integration by parts, but don't know what it's called or where it comes from. The trick is to find \lambda such that f'' = \lambda f and \mu such that g'' = \mu g, providing both are constants and \lambda\neq\mu. Then \intf(x)g(x)dx =...

I'm pretty sure this dog is less happy.

I only recently found this thread (and this site) and a few questions pop into my mind as I read. Well, actually just one. If we replaced the word "math" in the last eight pages with words or phrases like "singing", "foreign language acquisition", "painting", "(good) creative writing", or...

It's a moot point. If you see that three other drivers are going to reach the stop at the same time you do, just slow down or speed up to make sure the problem doesn't arise. That's what I do. Like I can't wait a few more seconds to get where I'm going?

35. If the monoliths have mass then they have gravity. Thus, with enough of them the added gravitational force will be enough to compress the hydrogen and initiate fusion, just as happens in the real universe.