Question Number 85600 by M±th+et£s last updated on 23/Mar/20 $$\int\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 23/Mar/20 $${I}\:=\int\:\frac{{x}^{\mathrm{2}} }{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 85601 by sahnaz last updated on 23/Mar/20 $$\int\frac{\mathrm{4u}}{\mathrm{4u}^{\mathrm{2}} −\mathrm{4u}+\mathrm{1}}\mathrm{du} \\ $$ Commented by Tony Lin last updated on 23/Mar/20 $$\int\frac{\mathrm{4}{u}}{\mathrm{4}{u}^{\mathrm{2}} −\mathrm{4}{u}+\mathrm{1}}{du} \\ $$$$=\frac{\mathrm{1}}{\mathrm{2}}\int\frac{\mathrm{8}{u}−\mathrm{4}}{\mathrm{4}{u}^{\mathrm{2}}…
Question Number 151132 by dw last updated on 18/Aug/21 $$ \\ $$$${Find}\:{the}\:{minimum}\:{value}\:{of}\:\:{x}\:,\:{if}\:\:\:\alpha<\mathrm{82}^{{o}} \:. \\ $$ Commented by dw last updated on 18/Aug/21 Terms of Service…
Question Number 85596 by M±th+et£s last updated on 23/Mar/20 $$\int\frac{\sqrt{{x}+\mathrm{1}}−\mathrm{1}}{\:\sqrt{{x}−\mathrm{1}}+\mathrm{1}}\:{dx} \\ $$ Commented by mathmax by abdo last updated on 23/Mar/20 $${A}\:=\int\:\:\frac{\sqrt{{x}+\mathrm{1}}−\mathrm{1}}{\:\sqrt{{x}−\mathrm{1}}+\mathrm{1}}{dx}\:\:\:\:{chagement}\:\sqrt{{x}−\mathrm{1}}+\mathrm{1}\:={t}\:{give}\:\sqrt{{x}−\mathrm{1}}={t}−\mathrm{1}\:\Rightarrow \\ $$$${x}−\mathrm{1}\:=\left({t}−\mathrm{1}\right)^{\mathrm{2}} \:\Rightarrow{dx}\:=\mathrm{2}\left({t}−\mathrm{1}\right){dt}\:\Rightarrow…
Question Number 20058 by Tinkutara last updated on 21/Aug/17 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{between}\:\oint\:\mathrm{and} \\ $$$$\int?\:\mathrm{Where}\:\mathrm{is}\:\oint\:\mathrm{used}? \\ $$ Answered by dioph last updated on 21/Aug/17 $$\oint\:\mathrm{indicates}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{is}\:\mathrm{calculated} \\ $$$$\mathrm{in}\:\:\mathrm{closed}\:\mathrm{path}.\:\mathrm{For}\:\mathrm{instance},\:\mathrm{for} \\…
Question Number 85592 by sahnaz last updated on 23/Mar/20 $$\int\frac{\left(\mathrm{u}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{u}^{\mathrm{3}} +\mathrm{u}}\mathrm{du} \\ $$ Answered by john santu last updated on 23/Mar/20 $$\int\:\frac{\mathrm{1}}{{x}}{dx}\:+\:\int\:\frac{\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\…
Question Number 85590 by sahnaz last updated on 23/Mar/20 $$\int\frac{\mathrm{1}+\mathrm{4u}}{−\mathrm{4u}^{\mathrm{2}} +\mathrm{2u}+\mathrm{2}}\mathrm{du} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85591 by sahnaz last updated on 23/Mar/20 $$\int\frac{\mathrm{1}+\mathrm{4u}}{−\mathrm{4u}^{\mathrm{2}} +\mathrm{2u}+\mathrm{2}}\mathrm{du} \\ $$$$ \\ $$ Answered by john santu last updated on 23/Mar/20 $$−\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{2}}{\mathrm{3}\left(\mathrm{2}{u}+\mathrm{1}\right)}{du}+\int\:\frac{\mathrm{5}}{\mathrm{3}\left({u}−\mathrm{1}\right)}{du} \\…
Question Number 20054 by Tinkutara last updated on 21/Aug/17 $$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\left(\alpha\:<\:\beta\right)\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:{x}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0},\:\mathrm{where} \\ $$$${c}\:<\:\mathrm{0}\:<\:{b},\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{0}\:<\:\alpha\:<\:\beta \\ $$$$\left(\mathrm{2}\right)\:\alpha\:<\:\mathrm{0}\:<\:\beta\:<\:\mid\alpha\mid \\ $$$$\left(\mathrm{3}\right)\:\alpha\:<\:\beta\:<\:\mathrm{0} \\ $$$$\left(\mathrm{4}\right)\:\alpha\:<\:\mathrm{0}\:<\:\mid\alpha\mid\:<\:\beta \\ $$…
Question Number 85588 by TawaTawa1 last updated on 23/Mar/20 Commented by john santu last updated on 23/Mar/20 $$\mathrm{14},\mathrm{450}\:=\:\frac{{a}\left(\mathrm{4}^{{n}} −\mathrm{1}\right)}{\mathrm{3}} \\ $$$$\mathrm{43},\mathrm{350}\:=\:{a}\:\left(\mathrm{4}^{{n}} −\mathrm{1}\right) \\ $$$${a}\:=\:\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}} −\mathrm{1}}\:\Rightarrow\:\mathrm{100}<\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}}…