Question Number 142191 by iloveisrael last updated on 27/May/21 Commented by Mathspace last updated on 27/May/21 $${why}\:{tan}\left(\frac{{x}}{\mathrm{2}}\right)={i}+\frac{\mathrm{2}{i}}{\mathrm{1}+{e}^{{ix}} }\:? \\ $$$${and}\:{what}\:{is}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\frac{{sin}\left({nx}\right)}{\mathrm{1}+{e}^{{ix}} }{dx} \\ $$$${all}\:{this}\:{need}\:{proof}……
Question Number 142176 by malwaan last updated on 27/May/21 $$\int\:{e}^{{ax}} \:{sin}\:{bx}\:{dx}\:=\:? \\ $$ Answered by Dwaipayan Shikari last updated on 27/May/21 $${sin}\left({bx}\right)=\frac{{e}^{{ibx}} −{e}^{−{ibx}} }{\mathrm{2}{i}} \\…
6-dx-x-2-3x-2-7-4dx-x-2-2x-4-8-3-2xdx-x-2-64-9-3x-1-x-3-5x-2-6x-dx-10-4-3x-x-3-2x-dx-11-dx-x-3-2x-x-
Question Number 142149 by cesarL last updated on 27/May/21 $$\mathrm{6}.\:\int\frac{{dx}}{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$$$\mathrm{7}.\:\int\frac{\mathrm{4}{dx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}} \\ $$$$\mathrm{8}.\:\int\frac{\mathrm{3}−\mathrm{2}{xdx}}{{x}^{\mathrm{2}} −\mathrm{64}} \\ $$$$\mathrm{9}.\:\int\frac{\mathrm{3}{x}−\mathrm{1}}{{x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} +\mathrm{6}{x}}{dx} \\ $$$$\mathrm{10}.\:\int\frac{\mathrm{4}−\mathrm{3}{x}}{{x}^{\mathrm{3}} −\mathrm{2}{x}}{dx} \\…
Question Number 76615 by mhmd last updated on 28/Dec/19 $$\int{sec}^{\mathrm{3}} {x}\:{dx} \\ $$ Answered by $@ty@m123 last updated on 28/Dec/19 $$\int\sqrt{\mathrm{1}+\mathrm{tan}\:^{\mathrm{2}} {x}}.\mathrm{sec}\:^{\mathrm{2}} {xdx} \\ $$$$\int\sqrt{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 142131 by Avijit007 last updated on 26/May/21 $$\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…