Question Number 81993 by msup trace by abdo last updated on 17/Feb/20 $${calculate}\:\int\int_{{D}} {ln}\left(\mathrm{1}+{x}+{y}\right){dxdy} \\ $$$${with}\:{D}\:{is}\:{the}\:{triangle}\:{limited}\:{by} \\ $$$${points}\:\mathrm{0},{A}\left(\mathrm{1},\mathrm{0}\right)\:{and}\:{B}\left(\mathrm{0},\mathrm{1}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 147487 by mnjuly1970 last updated on 21/Jul/21 $$ \\ $$$$ \\ $$$$\left({a}\:,\:\mathrm{2}{a}\:+\mathrm{1}\:\right]\cap\left[\:{a}^{\:\mathrm{2}} \:−{a}\:,\:{a}^{\:\mathrm{2}} +\:\mathrm{4}{a}\:+\mathrm{1}\:\right)\neq\:\varnothing \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{a}\:\in\:? \\ $$$$ \\ $$ Answered…
Question Number 147477 by vvvv last updated on 21/Jul/21 Commented by Rustambek last updated on 21/Jul/21 $${salom} \\ $$ Answered by puissant last updated on…
Question Number 81921 by M±th+et£s last updated on 16/Feb/20 Answered by MJS last updated on 16/Feb/20 $$\int\frac{\sqrt{\sqrt{{x}}+\sqrt{{x}−\mathrm{1}}}}{\:\sqrt{{x}}+\mathrm{1}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{{x}}+\sqrt{{x}−\mathrm{1}}\:\rightarrow\:{dx}=\frac{{t}^{\mathrm{4}} −\mathrm{1}}{\mathrm{2}{t}^{\mathrm{3}} }{dt}\right] \\ $$$$=\int\frac{\left({t}−\mathrm{1}\right)\left({t}^{\mathrm{2}} +\mathrm{1}\right)}{\:\sqrt{{t}^{\mathrm{3}} }\left({t}+\mathrm{1}\right)}{dt}=…
Question Number 81889 by rajesh4661kumar@gmail.com last updated on 16/Feb/20 Answered by john santu last updated on 16/Feb/20 $${let}\:\sqrt{{x}}\:=\:\mathrm{sin}\:{t}\:\Rightarrow{x}\:=\:\mathrm{sin}\:^{\mathrm{2}} {t} \\ $$$${dx}\:=\:\mathrm{2sin}\:{t}\:\mathrm{cos}\:{t}\:{dt}\: \\ $$$$\Rightarrow{I}\:=\:\int\:\sqrt{\frac{\mathrm{1}−\mathrm{sin}\:{t}}{\mathrm{1}+\mathrm{sin}\:{t}}\:}\:\left(\mathrm{2sin}\:{t}\:\mathrm{cos}\:{t}\:\right)\:{dt} \\ $$$$=\:\int\:\frac{\left(\mathrm{1}−\mathrm{sin}\:{t}\right)\mathrm{2sin}\:{t}\mathrm{cos}\:{t}}{\mathrm{cos}\:{t}}\:{dt}…
Question Number 81888 by rajesh4661kumar@gmail.com last updated on 16/Feb/20 Commented by mathmax by abdo last updated on 16/Feb/20 $${let}\:{A}\:=\int\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}}\:\:{we}\:{do}\:{the}\:{changement}\:{x}\:={cht}\:\Rightarrow \\ $$$${A}\:=\int\:\:\:\frac{{sht}\:{dt}}{\left({ch}^{\mathrm{2}} {t}\:+\mathrm{1}\right){sht}}\:=\int\:\:\frac{{dt}}{\mathrm{1}+\frac{\mathrm{1}+{ch}\left(\mathrm{2}{t}\right)}{\mathrm{2}}}\:=\int\:\:\frac{\mathrm{2}{dt}}{\mathrm{3}+{ch}\left(\mathrm{2}{t}\right)} \\…
Question Number 147399 by ArielVyny last updated on 20/Jul/21 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{{e}^{\mathrm{2}{arctg}\left({u}\right)} }{\:\sqrt{{u}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 81801 by Power last updated on 15/Feb/20 Commented by mathmax by abdo last updated on 16/Feb/20 $${changement}\:{x}^{{n}} \:={cos}^{\mathrm{2}} {t}\:{give}\:{x}\:=\left({cost}\right)^{\frac{\mathrm{2}}{{n}}} \:\Rightarrow{dx}\:=−\frac{\mathrm{2}}{{n}}{sint}\:\left({cost}\right)^{\frac{\mathrm{2}}{{n}}−\mathrm{1}} \\ $$$$\Rightarrow\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 147309 by puissant last updated on 19/Jul/21 Answered by mathmax by abdo last updated on 19/Jul/21 $$\mathrm{I}=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cosx}}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }\:\Rightarrow\mathrm{2I}=\int_{−\infty} ^{+\infty} \:\frac{\mathrm{cosx}}{\left(\mathrm{x}^{\mathrm{2}}…
Question Number 16240 by tawa tawa last updated on 19/Jun/17 Commented by tawa tawa last updated on 19/Jun/17 $$\mathrm{please}\:\mathrm{help}. \\ $$ Answered by ajfour last…