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 $${Let}\:{I}=\int\frac{\mathrm{2}{g}\left({x}\right){f}^{'} \left({x}\right)−{f}\left({x}\right){g}^{'} \left({x}\right)}{\mathrm{2}\left({g}\left({x}\right)\right)^{\mathrm{3}/\mathrm{2}} }{dx}. \\…
Question Number 5265 by Kasih last updated on 03/May/16 $$\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}} \\ $$$$\Rightarrow\int\frac{{x}}{\mathrm{1}+{x}}{dx}=\int\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+{x}}\right){dx}={x}−{ln}\mid{x}+\mathrm{1}\mid+{C} \\ $$$$ \\…
Question Number 5262 by Kasih last updated on 03/May/16 $$\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 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 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…
Question Number 136279 by aupo14 last updated on 20/Mar/21 Answered by mindispower last updated on 20/Mar/21 $$=\int{e}^{{x}+\frac{\mathrm{1}}{{x}}} {dx}+\int{x}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){e}^{{x}+\frac{\mathrm{1}}{{x}}} {dx}={A} \\ $$$$\mathrm{2}{nd}\:{by}\:{part} \\ $$$$\int{x}\left(\mathrm{1}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){e}^{{x}+\frac{\mathrm{1}}{{x}}}…
Question Number 5205 by Rojaye Shegz last updated on 30/Apr/16 $$\mathrm{Evaluate}; \\ $$$$\int\:\frac{\left({x}−{x}^{\mathrm{3}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} }{{x}^{\mathrm{4}} } \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 136267 by Algoritm last updated on 20/Mar/21 Commented by liberty last updated on 20/Mar/21 $$\int_{{e}} ^{\:{e}^{\mathrm{2}} } \sqrt{{x}+\frac{\mathrm{1}}{\mathrm{2}}\sqrt{{x}+\frac{\mathrm{1}}{\mathrm{4}}\sqrt{{x}+\frac{\mathrm{1}}{\mathrm{8}}\sqrt{…}}}}\:−\sqrt{{x}−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{{x}−\frac{\mathrm{1}}{\mathrm{4}}\sqrt{{x}−\frac{\mathrm{1}}{\mathrm{8}}\sqrt{…}}}}\:{dx} \\ $$ Terms of Service…
Question Number 70719 by oyemi kemewari last updated on 07/Oct/19 $$\int\mathrm{sin}\:\left(\mathrm{101x}\right)\mathrm{sin}\:^{\mathrm{99}} \mathrm{x}\:\mathrm{dx} \\ $$ Answered by mind is power last updated on 07/Oct/19 $${sin}\left(\mathrm{101}{x}\right)={sin}\left(\mathrm{100}{x}\right){cos}\left({x}\right)+{sin}\left({x}\right){cos}\left(\mathrm{100}{x}\right) \\…