That night, he wrote the substitution u = √(tan x). The page sighed. Then he let the pen rest. Some solutions are not answers. They are permission to stop. He closed the notebook and went to make tea. Please clarify which one you actually want (or both separately), and I’ll give a full response.
If you want all 100, I recommend finding Jim Coroneos' original booklet or checking online PDFs titled "100 Integrals (Worked Solutions)" – it's a known resource. Here is a very short literary draft: Title: The Last Integral coroneos 100 integrals worked solutions
∫ e^x cos x dx → Integration by parts twice (or use complex exponentials): result = (e^x (sin x + cos x))/2 + C That night, he wrote the substitution u = √(tan x)
∫ ln x dx → Integration by parts: u = ln x, dv = dx → du = (1/x) dx, v = x = x ln x - ∫ dx = x ln x - x + C Some solutions are not answers
"It's a trick," his granddaughter Mina said one winter evening, watching him erase for the tenth time.