Question Number 108789 by 150505R last updated on 19/Aug/20 Answered by 1549442205PVT last updated on 19/Aug/20 $$\mathrm{Choose}\:\mathrm{A}\:\mathrm{because}\:\int_{\mathrm{0}.\mathrm{5}} ^{\:\mathrm{1}} \frac{\mathrm{x}^{\mathrm{2}} }{\left(\mathrm{x}^{\mathrm{2}} −\mathrm{4}\right)\mathrm{sinx}+\mathrm{x4cox}}\mathrm{dx} \\ $$$$=\mathrm{ln}\mid\mathrm{cosec}\:\mathrm{2y}+\mathrm{coty}\mid_{\mathrm{0}.\mathrm{5}} ^{\mathrm{1}} =−\mathrm{1}.\mathrm{97}……
Question Number 108786 by 150505R last updated on 19/Aug/20 Answered by mathmax by abdo last updated on 19/Aug/20 $$\mathrm{first}\:\mathrm{we}\:\mathrm{study}\:\mathrm{the}\:\mathrm{convergence}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\mathrm{x}^{\mathrm{n}−\mathrm{1}\:} \mathrm{cos}\left(\mathrm{ax}\right)\mathrm{dx} \\ $$$$\mathrm{A}_{\mathrm{n}}…
Question Number 108761 by bemath last updated on 19/Aug/20 $$\:\:\:\frac{\vdots\frac{\mathcal{B}{e}}{\mathcal{M}{ath}}\vdots}{\bigstar} \\ $$$${If}\:\int_{−\mathrm{1}} ^{\:\:{a}} \:\frac{{x}+\mathrm{1}}{\left({x}+\mathrm{2}\right)^{\mathrm{4}} }\:=\:\frac{\mathrm{10}}{\mathrm{81}}\:,\:{then}\:{the}\:{value}\:{of} \\ $$$${a}−\mathrm{2}\:{is}\:\_\_\_ \\ $$ Answered by ajfour last updated on…
Question Number 108750 by mathmax by abdo last updated on 19/Aug/20 $$\mathrm{calculste}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}}\mathrm{dx} \\ $$ Answered by mnjuly1970 last updated on 19/Aug/20 $$\:\mathrm{sol}….:\:\mathrm{put}\::\:{x}=\frac{\mathrm{1}}{{t}}\Rightarrow\Omega=\:\int_{\mathrm{0}}…
Question Number 108748 by john santu last updated on 18/Aug/20 Answered by bemath last updated on 19/Aug/20 $$\:\:\:\:{by}\:{parts} \\ $$$$\:\begin{cases}{{u}=\mathrm{ln}\:\left(\mathrm{sin}\:{x}\right)\:\Rightarrow{du}=\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}}\:{dx}}\\{{v}=\int\:\mathrm{sin}\:{x}\:{dx}=−\mathrm{cos}\:{x}}\end{cases} \\ $$$${J}=−\mathrm{cos}\:{x}\:\mathrm{ln}\:\left(\mathrm{sin}\:{x}\right)+\int\:\frac{\mathrm{cos}\:^{\mathrm{2}} {x}\:{dx}}{\mathrm{sin}\:{x}} \\ $$$${J}=−\mathrm{cos}\:{x}\:\mathrm{ln}\:\left(\mathrm{sin}\:{x}\right)+\int\:\frac{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}}…
Question Number 108749 by mathmax by abdo last updated on 19/Aug/20 $$\mathrm{calculste}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\left(\mathrm{1}+\mathrm{x}\right)^{\mathrm{4}} }\:\mathrm{dx} \\ $$ Answered by mnjuly1970 last updated on 19/Aug/20 $${f}\left({a}\right)=\int_{\mathrm{0}}…
Question Number 108738 by mnjuly1970 last updated on 19/Aug/20 $$\:\:\:\:\:\:\:\:{please}:\:\:\:\:\:^{\ast} \mathrm{prove}^{\ast} :::: \\ $$$$\:\:\:\:\:\mathrm{1}.^{\mathrm{important}} \:\:\:\:\mathrm{lim}_{\mathrm{z}\rightarrow\mathrm{1}} \left(\zeta\:\left(\mathrm{z}\right)\:−\frac{\mathrm{1}}{\mathrm{z}−\mathrm{1}}\:\right)=\:\gamma\:\:\:\left(\mathrm{euler}\:\mathrm{constant}\right) \\ $$$$\:\:\:\:\mathrm{2}.\:\overset{\mathrm{important}} {\:}\:\:\int_{\mathrm{0}} ^{\:\infty} \left(\mathrm{cos}\left(\mathrm{x}\right)−\frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\right)\frac{\mathrm{dx}}{\mathrm{x}}\:=−\:\gamma \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..\mathscr{M}.\mathscr{N}….. \\…
Question Number 43191 by MASANJA J last updated on 08/Sep/18 $${integrate}\:{by}\:{use}\:{a}\:{partial}\:{friction} \\ $$$$\int\frac{{lnx}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} } \\ $$ Commented by mondodotto@gmail.com last updated on 09/Sep/18 $$\mathrm{did}\:\mathrm{you}\:\mathrm{mean}\:\mathrm{by}\:\mathrm{parts}? \\…
Question Number 43190 by MASANJA J last updated on 08/Sep/18 $${a}\:{point}\:{move}\:{in}\:{such}\:{away}\:{that}\:{its}\: \\ $$$${its}\:{distance}\:{from}\:{the}\:{x}−{axis}\:{is}\:{alwa} \\ $$$${yas}\frac{\mathrm{1}}{\mathrm{5}}\:{its}\:{distance}\:{from}\:{origin}. \\ $$$${find}\:{the}\:{equetion}\:{of}\:{its}\:{path}. \\ $$ Commented by MrW3 last updated on…
Question Number 108723 by 150505R last updated on 18/Aug/20 Commented by bemath last updated on 19/Aug/20 $${I}=\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\:\mathrm{ln}\:\left(\sqrt{\mathrm{2}}\:\mathrm{cos}\:\:\left({x}−\frac{\pi}{\mathrm{4}}\right)\right){dx} \\ $$$$\:=\:\left[\:{x}\:\mathrm{ln}\:\left(\sqrt{\mathrm{2}}\right)\:\right]_{\mathrm{0}} ^{\pi/\mathrm{2}} +\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}\mathrm{ln}\:\left(\mathrm{cos}\:\:\left({x}−\frac{\pi}{\mathrm{4}}\right)\right){dx}…