Question Number 142131 by Avijit007 last updated on 26/May/21 $$\int\frac{{dx}}{\mathrm{3}+\mathrm{2}{sinx}+{cosx}}{dx} \\ $$ Commented by Avijit007 last updated on 26/May/21 $${help} \\ $$ Answered by 676597498…
Question Number 142120 by bekzodjumayev last updated on 26/May/21 Commented by bekzodjumayev last updated on 26/May/21 $${Help} \\ $$ Commented by Avijit007 last updated on…
Question Number 142116 by Eric002 last updated on 26/May/21 $${use}\:{trigonometric}\:{substitution}\:{to}\:{solve} \\ $$$$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }}{dx} \\ $$ Answered by ZiYangLee last updated on 27/May/21 $$\int\frac{{x}^{\mathrm{3}} }{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}}…
Question Number 11042 by Mahmoud A.R last updated on 09/Mar/17 $$\int{cos}\left({x}\right)\sqrt{\frac{{sin}\left({x}\right)+\mathrm{1}}{{sin}\left({x}\right)−\mathrm{1}}\:}\:{dx} \\ $$ Answered by ajfour last updated on 09/Mar/17 $$\:\:\int\mathrm{cos}\:\left({x}\right)\sqrt{−\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{1}−\mathrm{sin}\:{x}}}\:{dx} \\ $$$$=\sqrt{−\mathrm{1}}\:\int\mathrm{cos}\:\left({x}\right)\sqrt{\frac{\left(\mathrm{1}+\mathrm{sin}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)}{\left(\mathrm{1}−\mathrm{sin}\:{x}\right)\left(\mathrm{1}+\mathrm{sin}\:{x}\right)}}\:{dx} \\ $$$$=\:{i}\int\mathrm{cos}\:\left({x}\right)\left(\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\right){dx}…
Question Number 76572 by john santu last updated on 28/Dec/19 $${how}\:{do}\:{you}\:{find}\:{the}\:{least}\:{value}\:{of}\:{x}^{\mathrm{2}} \\ $$$$+\mathrm{2}{xy}+\mathrm{3}{y}^{\mathrm{2}} −\mathrm{6}{x}−\mathrm{2}{y}\:{using}\:{the}\: \\ $$$${concepts}\:{of}\:{algebra}\:{or}\:{calculus}?\: \\ $$ Answered by benjo 1/2 santuyy last updated…
Question Number 142103 by rs4089 last updated on 26/May/21 $$\int_{−\infty} ^{\infty} \frac{{tan}^{−\mathrm{1}} \left(\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{2}}}{dx} \\ $$ Answered by mathmax by abdo last updated…
Question Number 142060 by iloveisrael last updated on 26/May/21 Answered by Ar Brandon last updated on 26/May/21 $$\mathrm{I}=\int\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \mathrm{sec}\left(\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \right)\mathrm{tan}\left(\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \right)\mathrm{dx} \\ $$$${u}=\mathrm{1}+\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{x}}} \Rightarrow\mathrm{d}{u}=−\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}}…
Question Number 142028 by mnjuly1970 last updated on 25/May/21 $$\:\:\:\:\:\:\:\:…………{Calculus}………\: \\ $$$$\:\:\:\:\:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({sin}\left({x}\right)\right).{e}^{{cos}\left({x}\right)} }{{x}}{dx}=??? \\ $$$$\:…………{m}.{n}….. \\ $$ Answered by mindispower last updated on…
Question Number 76468 by kaivan.ahmadi last updated on 27/Dec/19 $$\int\frac{\mathrm{1}−{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}}{{x}^{\mathrm{4}} −{x}^{\mathrm{3}} −{x}+\mathrm{1}}{dx} \\ $$ Commented by mr W last updated on 27/Dec/19 $${why}\:{did}\:{you}\:{write}\:\mathrm{1}−{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{1}…
Question Number 76467 by kaivan.ahmadi last updated on 27/Dec/19 $$\int\frac{{dx}}{\:\sqrt{{e}^{\mathrm{2}{x}} −\mathrm{4}}\left({sec}^{−\mathrm{1}} \left(\frac{{e}^{{x}} }{\mathrm{4}}\right)\right)} \\ $$ Answered by john santu last updated on 28/Dec/19 $${let}\::\mathrm{sec}\:{u}\:=\:\frac{{e}^{{x}} }{\mathrm{4}}\:\rightarrow\:{e}^{{x}}…