Question Number 70818 by oyemi kemewari last updated on 08/Oct/19 $$\mathrm{what}\:\mathrm{the}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\int_{\mathrm{a}} ^{\mathrm{b}} \mathrm{f}\left(\mathrm{a}+\mathrm{b}−\mathrm{x}\right)\:\mathrm{dx} \\ $$ Commented by kaivan.ahmadi last updated on…
Question Number 5278 by sara last updated on 04/May/16 $$\int\left\{\left(\mathrm{3}{x}\right){i}+\left(\mathrm{2}{x}\right){y}\right\}{dx}= \\ $$$$ \\ $$ Answered by FilupSmith last updated on 04/May/16 $$\int\left(\mathrm{3}{xi}+\mathrm{2}{xy}\right){dx} \\ $$$$=\mathrm{3}{i}\int{xdx}+\mathrm{2}{y}\int{xdx} \\…
Question Number 70808 by rajesh4661kumar@gmail.com last updated on 08/Oct/19 Answered by MJS last updated on 08/Oct/19 $$\int\left(\mathrm{sec}\:{x}\right)^{\frac{\mathrm{2}}{\mathrm{3}}} \left(\mathrm{csc}\:{x}\right)^{\frac{\mathrm{4}}{\mathrm{3}}} {dx}=\int\frac{{dx}}{\mathrm{sin}\:{x}\:\mathrm{cos}\:{x}\:\left(\mathrm{tan}\:{x}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} }= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\:\rightarrow\:{dx}=\left(\mathrm{cos}\:{x}\right)^{\mathrm{2}} {dt}\right] \\ $$$$=\int\frac{{dt}}{{t}^{\frac{\mathrm{4}}{\mathrm{3}}}…
Question Number 5266 by Kasih last updated on 03/May/16 $$\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} \\ $$$$\frac{\mathrm{3}{x}+\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{5}}}−\frac{\mathrm{3}}{\:\sqrt{{x}^{\mathrm{2}}…
Question Number 136343 by snipers237 last updated on 21/Mar/21 $$\:\:\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}!\: \\ $$ Answered by mindispower last updated on 21/Mar/21…
Question Number 136333 by Bird last updated on 20/Mar/21 $${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 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}…