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find-the-three-last-digits-of-7-2020-

Question Number 86025 by Maclaurin Stickker last updated on 26/Mar/20 $${find}\:{the}\:{three}\:{last}\:{digits}\:{of}\:\:\mathrm{7}^{\mathrm{2020}} . \\ $$ Commented by MJS last updated on 26/Mar/20 $$\mathrm{you}\:\mathrm{can}\:\mathrm{do}\:\mathrm{it}\:\mathrm{yourself}.\:\mathrm{find}\:\mathrm{out},\:\mathrm{after}\:\mathrm{how} \\ $$$$\mathrm{many}\:\mathrm{steps}\:\mathrm{the}\:\mathrm{digits}\:\mathrm{repeat} \\…

ln-sinx-x-0-2kpi-k-Z-

Question Number 151486 by mathocean1 last updated on 21/Aug/21 $$\int{ln}\left({sinx}\right)=?\: \\ $$$${x}\:\neq\:\mathrm{0}\:+\:\mathrm{2}{k}\pi\:;\:{k}\:\in\:\mathbb{Z} \\ $$ Answered by Olaf_Thorendsen last updated on 21/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\mathrm{ln}\left(\mathrm{sin}{x}\right)\:{dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:{x}\mathrm{ln}\left(\mathrm{sin}{x}\right)−\int{x}\mathrm{cot}{x}\:{dx} \\…

Question-20364

Question Number 20364 by mondodotto@gmail.com last updated on 26/Aug/17 Answered by Tinkutara last updated on 26/Aug/17 $$\mathrm{59}\:=\:\mathrm{77}\:−\:\left(\mathrm{6}\:+\:\mathrm{3}{x}\right)\:+\:{x} \\ $$$$\mathrm{2}{x}\:=\:\mathrm{12} \\ $$$${x}\:=\:\mathrm{6} \\ $$ Commented by…