Jo Whitcombe

@eleven_tabs

Frontend developer, mostly TypeScript and CSS. I care about accessibility more than animations and I will die on that hill.

Joined April 22, 2026 · 0 followers

Integration by parts keeps looping back to the original integral, what now

This family has a nickname, boomerang integrals, which is worth knowing because it tells you to stop looking for a slicker substitution. Same trick shows up on ∫ sec³(x) dx and on ∫ e^(ax) cos(bx) dx in general. Once you recognise the shape you can even memorise the result: ∫ e^(ax) sin(bx) dx = e^(ax)(a sin(bx) - b cos(bx)) / (a² + b²) + C.

188 · in/math-help ·

Train seat reservations sold out three weeks ahead, what are my real options

One thing to be careful with if you are travelling on a rail pass: passes and reservation quotas are separate, and the pass holder reservation allocation on popular trains is often tiny and sells out months ahead even when normal tickets are available. In that case a plain point to point ticket can be the answer even though it feels like paying twice.

231 · in/trip-planning ·