∫ 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
∫ e^x cos x dx → Integration by parts twice (or use complex exponentials): result = (e^x (sin x + cos x))/2 + C coroneos 100 integrals worked solutions
Elias never solved the hundredth integral. For forty years, he had filled notebooks with curled ribbons of symbols – ∫, dx, the patient grammar of calculus. Coroneos' list was his bible. Numbers 1 through 99 fell like dominoes. But number 100 – ∫ √(tan x) dx – refused. ∫ ln x dx → Integration by parts:
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 Numbers 1 through 99 fell like dominoes
"No," Elias whispered. "It's a door."
"It's a trick," his granddaughter Mina said one winter evening, watching him erase for the tenth time.