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}…
Question Number 136331 by mohammad17 last updated on 20/Mar/21 Answered by mr W last updated on 20/Mar/21 $$\mathrm{5}×\mathrm{3}^{{n}+\mathrm{1}} ×\mathrm{2}^{\mathrm{1}−\mathrm{2}{n}} \\ $$$$=\mathrm{5}×\mathrm{3}^{{n}} ×\mathrm{3}×\mathrm{2}×\mathrm{4}^{−{n}} \\ $$$$=\mathrm{30}×\left(\frac{\mathrm{3}}{\mathrm{4}}\overset{{n}} {\right)}…
Question Number 136325 by frc2crc last updated on 20/Mar/21 $${please}\:{a}\:{generall}\:{Form}\:{for}\:{C}\left({n}\right) \\ $$$${C}\left({n}\right)=\frac{\mathrm{4}}{\pi^{\mathrm{2}} }\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} \zeta\left(\mathrm{2}{k}\right)\zeta\left(\mathrm{2}{n}−\mathrm{2}{k}\right) \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 5254 by Rasheed Soomro last updated on 02/May/16 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which} \\ $$$$\left(\boldsymbol{\mathrm{a}}\right)\:\mathrm{5}\:\mathrm{children}\:\mathrm{can}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{groups} \\ $$$$\mathrm{of}\:\mathrm{2}\:\mathrm{and}\:\mathrm{3}\:, \\ $$$$\left(\boldsymbol{\mathrm{b}}\right)\:\mathrm{9}\:\mathrm{children}\:\mathrm{can}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{groups} \\ $$$$\mathrm{of}\:\mathrm{5}\:\mathrm{and}\:\mathrm{4}, \\ $$$$\mathrm{Hence}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in} \\ $$$$\mathrm{which}\:\mathrm{9}\:\mathrm{children}\:\mathrm{can}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into} \\ $$$$\mathrm{groups}\:\mathrm{of}\:\mathrm{2},\mathrm{3}\:\mathrm{and}\:\mathrm{4}.…
Question Number 136320 by radians last updated on 20/Mar/21 Answered by Olaf last updated on 20/Mar/21 $$\mathrm{coefficient}\:{x}^{\mathrm{2}} \:\mathrm{is}\:\mathrm{same}\:\mathrm{as}\:{x}^{\mathrm{3}} \:: \\ $$$$\Rightarrow\:\mathrm{C}_{\mathrm{2}} ^{\mathrm{2020}} {a}^{\mathrm{2}} {b}^{\mathrm{2018}} \:=\:\mathrm{C}_{\mathrm{3}}…
Question Number 70784 by rajesh4661kumar@gmail.com last updated on 08/Oct/19 Commented by MJS last updated on 08/Oct/19 $$\mathrm{really}\:\frac{{x}+\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{3}\sqrt{{x}+\mathrm{1}}}\:\mathrm{not}\:\frac{{x}+\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{3}\right)\sqrt{{x}+\mathrm{1}}}? \\ $$ Commented by rajesh4661kumar@gmail.com last…