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Author: Tinku Tara

Prove-that-a-b-c-d-a-c-d-b-

Question Number 1483 by Rasheed Ahmad last updated on 13/Aug/15 $$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{a}+\left(\mathrm{b}+\mathrm{c}\right)+\mathrm{d}=\left(\mathrm{a}+\mathrm{c}\right)+\left(\mathrm{d}+\mathrm{b}\right) \\ $$ Commented by prakash jain last updated on 13/Aug/15 $$\mathrm{Basic}\:\mathrm{properties}\:\mathrm{of}\:+\:\mathrm{operator}.\:\mathrm{Or}\:\mathrm{is}\:\mathrm{it} \\…

Question-132554

Question Number 132554 by mohammad17 last updated on 15/Feb/21 Commented by MJS_new last updated on 15/Feb/21 $$\mathrm{we}\:\mathrm{had}\:\mathrm{this}\:\mathrm{many}\:\mathrm{times}\:\mathrm{before}.\:\mathrm{simply} \\ $$$$\mathrm{substitute}\:{t}=\sqrt{\mathrm{tan}\:\theta}\:\mathrm{and}\:\mathrm{there}\:\mathrm{you}\:\mathrm{go} \\ $$ Commented by liberty last…

find-arctan-1-x-1-dx-

Question Number 67017 by mathmax by abdo last updated on 21/Aug/19 $${find}\:\int\:\:{arctan}\left(\mathrm{1}+\sqrt{{x}+\mathrm{1}}\right){dx} \\ $$ Commented by mathmax by abdo last updated on 24/Aug/19 $${let}\:{I}\:=\int\:{arctan}\left(\mathrm{1}+\sqrt{{x}+\mathrm{1}}\right){dx}\:\:{changement}\:\sqrt{{x}+\mathrm{1}}={t}\:{give}\:{x}+\mathrm{1}={t}^{\mathrm{2}} \:\Rightarrow…

John-and-Ghina-have-a-date-at-a-given-time-and-each-will-arrive-at-the-meeting-place-with-a-delay-between-0-and-1-hour-with-all-pairs-of-delays-being-equally-likely-The-first-arrive-will-wait-for-1

Question Number 132548 by liberty last updated on 15/Feb/21 $$\mathrm{John}\:\mathrm{and}\:\mathrm{Ghina}\:\mathrm{have}\:\mathrm{a}\:\mathrm{date}\:\mathrm{at} \\ $$$$\mathrm{a}\:\mathrm{given}\:\mathrm{time},\:\mathrm{and}\:\mathrm{each}\:\mathrm{will}\:\mathrm{arrive} \\ $$$$\mathrm{at}\:\mathrm{the}\:\mathrm{meeting}\:\mathrm{place}\:\mathrm{with}\:\mathrm{a}\:\mathrm{delay}\:\mathrm{between} \\ $$$$\mathrm{0}\:\mathrm{and}\:\mathrm{1}\:\mathrm{hour},\:\mathrm{with}\:\mathrm{all}\:\mathrm{pairs}\:\mathrm{of} \\ $$$$\mathrm{delays}\:\mathrm{being}\:\mathrm{equally}\:\mathrm{likely}. \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{arrive}\:\mathrm{will}\:\mathrm{wait}\:\mathrm{for} \\ $$$$\mathrm{15}\:\mathrm{minutes}\:\mathrm{and}\:\mathrm{will}\:\mathrm{leave}\:\mathrm{if} \\ $$$$\mathrm{the}\:\mathrm{other}\:\mathrm{has}\:\mathrm{not}\:\mathrm{yet}\:\mathrm{arrived}.\:\mathrm{What} \\…