Question Number 136346 by ZiYangLee last updated on 21/Mar/21 $$\mathrm{If}\:\mathrm{1},\omega\:\mathrm{and}\:\omega^{\mathrm{2}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{cube}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{unity}, \\ $$$$\mathrm{prove}\:\mathrm{that}\:\left(\mathrm{1}−\omega\right)\left(\mathrm{1}−\omega^{\mathrm{2}} \right)\left(\mathrm{1}−\omega^{\mathrm{4}} \right)\left(\mathrm{1}−\omega^{\mathrm{5}} \right)=\mathrm{9} \\ $$ Answered by Rasheed.Sindhi last updated on 21/Mar/21…
Question Number 136340 by liberty last updated on 21/Mar/21 $${If}\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}}\:=\:\sqrt{\frac{{a}+\sqrt{{b}}}{{c}}}\:+\:\sqrt{\frac{{a}−\sqrt{{b}}}{{c}}} \\ $$$${then}\:{a}+{bc}\:=\:? \\ $$ Answered by Ñï= last updated on 21/Mar/21 $$\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}}=\sqrt{{x}}+\sqrt{{y}} \\ $$$$\mathrm{3}+\sqrt{\mathrm{2}}={x}+{y}+\mathrm{2}\sqrt{{xy}} \\…
Question Number 136343 by snipers237 last updated on 21/Mar/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{2021}} }{{x}−{ln}\left(\underset{{k}=\mathrm{0}} {\overset{\mathrm{2020}} {\sum}}\frac{{x}^{{k}} }{{k}!}\right)}\:\overset{?} {=}\:\mathrm{2021}!\: \\ $$ Answered by mindispower last updated on 21/Mar/21…
Question Number 5266 by Kasih last updated on 03/May/16 $$\int\:\frac{\mathrm{3}{x}}{\:\sqrt{{x}^{\mathrm{2}} +\:\mathrm{2}{x}+\:\mathrm{5}}}\:{dx} \\ $$ Commented by prakash jain last updated on 03/May/16 $$\mathrm{You}\:\mathrm{can}\:\mathrm{integrate}\:\mathrm{as}\:\mathrm{following} \\ $$$$\frac{\mathrm{3}{x}+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}}}−\frac{\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 5265 by Kasih last updated on 03/May/16 $$\int\:\frac{{x}}{\mathrm{1}+{x}}\:{dx} \\ $$ Answered by Yozzii last updated on 03/May/16 $$\frac{{x}}{\mathrm{1}+{x}}=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+{x}}=\frac{\mathrm{1}+{x}−\mathrm{1}}{\mathrm{1}+{x}}=\frac{{x}}{\mathrm{1}+{x}} \\ $$$$\Rightarrow\int\frac{{x}}{\mathrm{1}+{x}}{dx}=\int\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+{x}}\right){dx}={x}−{ln}\mid{x}+\mathrm{1}\mid+{C} \\ $$$$ \\…
Question Number 5264 by Kasih last updated on 03/May/16 $${Prove}\:{that}\:\int\:\frac{\mathrm{2}{g}\left({x}\right){f}'\left({x}\right)−{f}\left({x}\right){g}'\left({x}\right)}{\mathrm{2}\left({g}\left({x}\right)\right)^{\frac{\mathrm{3}}{\mathrm{2}}} }\:{dx}\:=\frac{{f}\left({x}\right)}{\:\sqrt{{g}\left({x}\right)}}\:+\:{C} \\ $$ Answered by Yozzii last updated on 03/May/16 $${Let}\:{I}=\int\frac{\mathrm{2}{g}\left({x}\right){f}^{'} \left({x}\right)−{f}\left({x}\right){g}^{'} \left({x}\right)}{\mathrm{2}\left({g}\left({x}\right)\right)^{\mathrm{3}/\mathrm{2}} }{dx}. \\…
Question Number 136333 by Bird last updated on 20/Mar/21 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{t}^{{a}} }{\mathrm{1}+{t}+{t}^{\mathrm{2}} }{dt} \\ $$$${study}\:{first}\:{the}\:{convergence} \\ $$$$\left({a}\:{real}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 70798 by jagannath19 last updated on 08/Oct/19 Commented by jagannath19 last updated on 08/Oct/19 $${with}\:{explanation}\:{please}\:{sir} \\ $$ Answered by mind is power last…
Question Number 5262 by Kasih last updated on 03/May/16 $$\int\mathrm{cos}^{\mathrm{3}} {x}\sqrt{\mathrm{sin}{x}}{dx} \\ $$ Answered by Yozzii last updated on 03/May/16 $${J}=\int{cos}^{\mathrm{3}} {x}\sqrt{{sinx}}{dx}=\int{cosxcos}^{\mathrm{2}} {x}\sqrt{{sinx}}{dx} \\ $$$${J}=\int{cosx}\left(\mathrm{1}−{sin}^{\mathrm{2}}…
Question Number 5261 by Kasih last updated on 03/May/16 $$\int{x}^{\mathrm{2014}} \mathrm{sin}\left({x}^{\mathrm{2015}} +\mathrm{2015}\right) \\ $$ Answered by Yozzii last updated on 03/May/16 $${Let}\:{u}={x}^{{n}} +{c}\Rightarrow{du}={nx}^{{n}−\mathrm{1}} {dx}\Rightarrow\frac{\mathrm{1}}{{n}}{du}={x}^{{n}−\mathrm{1}} {dx}…