Studying Mathematics Thread

[polymath257]

This took quite a bit of effort, but here's how you derive the integral of secx "from scratch". Whoever came up with such solution was pretty damn smart.

Here's the work (thanks to YouTube, of course!):
https://pasteboard.co/HiEZbdk.png

That's the cursor at the end of the last line (not an absolute value bar).

Much easier is to realize that the derivative of

sec x + tan x

is

sec x tan x + sec^2 x = sec x(sec x + tan x).

So, write

int sec x dx = int [ sec x (sec x + tan x) ]/(sec x + tan x) dx

and do a substitution u= sec x + tan x. The result falls out.