Question Number 151345 by peter frank last updated on 20/Aug/21 $$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{e}^{\mathrm{cos}\:\mathrm{x}} }{\mathrm{e}^{\mathrm{cos}\:\mathrm{x}} +\mathrm{e}^{−\mathrm{cos}\:\mathrm{x}} }\mathrm{dx} \\ $$ Answered by Olaf_Thorendsen last updated on 20/Aug/21…
Question Number 151344 by mathdanisur last updated on 20/Aug/21 $$\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{4x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\:\Rightarrow\:\:\mathrm{x}^{\mathrm{3}} \:+\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }\:=\:? \\ $$ Answered by dumitrel last updated on 20/Aug/21 $${x}−\mathrm{4}+\frac{\mathrm{1}}{{x}}=\mathrm{0}\Rightarrow{x}+\frac{\mathrm{1}}{{x}}=\mathrm{4}\Rightarrow \\ $$$$\mathrm{64}={x}^{\mathrm{3}}…
Question Number 151346 by mathdanisur last updated on 20/Aug/21 $$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{5x}\:+\:\mathrm{25}\:=\:\mathrm{0}\:\:\Rightarrow\:\:\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{100}\:=\:? \\ $$ Answered by Rasheed.Sindhi last updated on 20/Aug/21 $$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{5x}\:+\:\mathrm{25}\:=\:\mathrm{0}\:\:\Rightarrow\:\:\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{100}\:=\:? \\…
Question Number 151341 by peter frank last updated on 20/Aug/21 $$\int_{\alpha} ^{\beta} \frac{\mathrm{dx}}{\mathrm{x}\sqrt{\left(\mathrm{x}−\alpha\right)\left(\beta−\mathrm{x}\right)\:}}=\frac{\pi}{\:\sqrt{\alpha\beta}} \\ $$$$\mathrm{where}\:\alpha,\beta\:>\mathrm{0} \\ $$ Answered by Kamel last updated on 20/Aug/21 $$…
Question Number 151340 by peter frank last updated on 20/Aug/21 $$\mathrm{Evaluate} \\ $$$$\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\left(\mathrm{2x}^{\mathrm{332}} +\mathrm{x}^{\mathrm{998}} +\mathrm{4x}^{\mathrm{1668}} .\mathrm{sin}\:\mathrm{x}^{\mathrm{691}} \right)}{\mathrm{1}+\mathrm{x}^{\mathrm{666}} }\mathrm{dx} \\ $$ Answered by qaz…
Question Number 85807 by jagoll last updated on 25/Mar/20 $$\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{x}^{\mathrm{2}} \:\mathrm{dx}}{\:\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{4}} }} \\ $$ Answered by Joel578 last updated on 25/Mar/20 $${I}\:\:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}}…
Question Number 85801 by mathmax by abdo last updated on 24/Mar/20 $${calculate}\:\int_{\mathrm{0}} ^{\pi} \:\:\frac{{dx}}{\left({cosx}\:+\mathrm{2}{sinx}\right)^{\mathrm{2}} } \\ $$ Commented by john santu last updated on 25/Mar/20…
Question Number 151332 by mathdanisur last updated on 20/Aug/21 $$\mathrm{which}\:\mathrm{is}\:\mathrm{larger}? \\ $$$$\mathrm{2}^{\sqrt{\mathrm{10}}} \:\:\mathrm{or}\:\:\mathrm{3}^{\mathrm{2}} \\ $$ Commented by liberty last updated on 20/Aug/21 $$\mathrm{3}^{\mathrm{2}} \\ $$…
Question Number 20259 by Tinkutara last updated on 24/Aug/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{real}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{2}{x}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$ Answered by ajfour last updated on 24/Aug/17 $${f}\:'\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\:>\mathrm{0}…
Question Number 20257 by tammi last updated on 24/Aug/17 $$\int\frac{{dx}}{\left(\mathrm{1}−{x}\right)\sqrt{\mathrm{1}+{x}}} \\ $$ Answered by Tinkutara last updated on 24/Aug/17 $${t}^{\mathrm{2}} \:=\:{x}\:+\:\mathrm{1} \\ $$$${dx}\:=\:\mathrm{2}{tdt} \\ $$$$\int\frac{\mathrm{2}{tdt}}{\left(\mathrm{2}\:−\:{t}^{\mathrm{2}}…