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x-1-x-2-x-12-

Question Number 151999 by otchereabdullai@gmail.com last updated on 24/Aug/21 $$\int\frac{\mathrm{x}−\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{12}} \\ $$ Answered by Olaf_Thorendsen last updated on 25/Aug/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} +{x}−\mathrm{12}}\:{dx} \\ $$$$\mathrm{F}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}\int\left(\frac{\mathrm{2}{x}+\mathrm{1}}{{x}^{\mathrm{2}} +{x}−\mathrm{12}}−\frac{\mathrm{3}}{{x}^{\mathrm{2}}…

Question-20876

Question Number 20876 by ajfour last updated on 05/Sep/17 Commented by ajfour last updated on 05/Sep/17 $${Rod}\:{AB}\:{is}\:{initially}\:{on}\:{a}\:{tabletop}. \\ $$$${End}\:{a}\:{given}\:{only}\:{a}\:{little}\:{push}\:{to} \\ $$$${start}\:{the}\:{fall}\:{of}\:{the}\:{rod}\:{as}\:{it}\:{turns} \\ $$$${through}\:{end}\:{B}\:{where}\:{static}\:{friction} \\ $$$${coefficient}\:{is}\:{high}\:{enough}.…

Prove-arctan1-arctan2-arctan3-pi-

Question Number 151943 by Huy last updated on 24/Aug/21 $$\mathrm{Prove}\:\mathrm{arctan1}+\mathrm{arctan2}+\mathrm{arctan3}=\pi \\ $$ Commented by puissant last updated on 24/Aug/21 $${x}={arctan}\mathrm{1}\:,\:{y}={arctan}\mathrm{2}\:,\:{z}={arctan}\mathrm{3} \\ $$$${p}={x}+{y} \\ $$$$\Rightarrow\:{tan}\left({p}\right)={tan}\left({x}+{y}\right)=\frac{{tanx}+{tany}}{\mathrm{1}−{tanxtany}} \\…

Question-151876

Question Number 151876 by tabata last updated on 23/Aug/21 Answered by Olaf_Thorendsen last updated on 23/Aug/21 $$\mathrm{A}\:=\:\mathrm{0}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{3}}{\mathrm{5}}+\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{5}}{\mathrm{7}}+… \\ $$$$\mathrm{A}\:=\:\frac{\mathrm{0}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{4}}+\frac{\mathrm{3}}{\mathrm{5}}+\frac{\mathrm{4}}{\mathrm{6}}+\frac{\mathrm{5}}{\mathrm{7}}+… \\ $$$$\mathrm{A}\:=\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{n}}{{n}+\mathrm{2}}\:\:\:\mathrm{diverges} \\ $$…