Question Number 31516 by abdo imad last updated on 09/Mar/18 $${find}\:\int\:\:\:\frac{{dx}}{{x}\:+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:. \\ $$ Commented by abdo imad last updated on 16/Mar/18 $${I}\:=\:\int\:\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:−{x}\right){dx}=\:\int\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\:{dx}\:−\frac{{x}^{\mathrm{2}}…
Question Number 31515 by abdo imad last updated on 09/Mar/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{dx}}{{chx}}\:. \\ $$ Commented by abdo imad last updated on 10/Mar/18 $${I}=\:\int_{\mathrm{0}} ^{\mathrm{1}}…
Question Number 31514 by abdo imad last updated on 09/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{arctan}\left(\mathrm{2}{x}\right)}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }{dx}. \\ $$ Answered by sma3l2996 last updated on 10/Mar/18 $${by}\:{parts}\: \\…
Question Number 31512 by abdo imad last updated on 09/Mar/18 $${find}\:{lim}_{{x}\rightarrow\infty} \:\int_{{x}} ^{\mathrm{2}{x}} \:\:\frac{{cos}\left(\frac{\mathrm{1}}{{t}}\right)}{{t}}\:{dt}. \\ $$ Commented by abdo imad last updated on 12/Mar/18 $$\left.\exists\:{c}\:\in\right]{x},\mathrm{2}{x}\left[\:/\:\int_{{x}}…
Question Number 31513 by abdo imad last updated on 09/Mar/18 $${find}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{\mathrm{2}\:+{cosx}}\:\:. \\ $$ Commented by abdo imad last updated on 10/Mar/18 $${the}\:{ch}.\:{e}^{{ix}} ={z}\:{give}…
Question Number 31506 by abdo imad last updated on 09/Mar/18 $${let}\:{f}\left({x}\right)=\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{sht}}{{t}}{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:{f}\left({x}\right)\:. \\ $$ Commented by abdo imad…
Question Number 31507 by abdo imad last updated on 09/Mar/18 $${g}\:{is}\:{real}\:{function}\:{continue}\:{let} \\ $$$${f}\left({x}\right)=\int_{\mathrm{0}} ^{{x}} \:{sin}\left({x}−{t}\right){g}\left({t}\right){dt} \\ $$$$\left.\mathrm{1}\right){prove}\:{that}\:{f}^{'} \left({x}\right)=\:\int_{\mathrm{0}} ^{{x}} {cos}\left({t}−{x}\right){g}\left({t}\right){dt} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:{f}\:{is}\:{so}<{ution}\:{of}\:{the}\:{diff}.{equa}. \\ $$$${y}^{''} \:+{y}\:={g}\left({x}\right)…
Question Number 31504 by abdo imad last updated on 09/Mar/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{{dt}}{{t}\:+\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}\:. \\ $$ Commented by abdo imad last updated on 15/Mar/18 $${let}\:{put}\:{t}={sinx}\:\Rightarrow\:{I}=\int_{\mathrm{0}}…
Question Number 97041 by bemath last updated on 06/Jun/20 $$\int\:\mathrm{sin}\:^{\mathrm{8}} \left({x}\right)\:\mathrm{cos}\:^{\mathrm{8}} \left({x}\right)\:{dx}\:=\:? \\ $$ Answered by john santu last updated on 06/Jun/20 $$\Rightarrow\mathrm{sin}\:^{\mathrm{8}} {x}.\mathrm{cos}\:^{\mathrm{8}} {x}\:=\:\frac{\mathrm{sin}\:^{\mathrm{8}}…
Question Number 31505 by abdo imad last updated on 09/Mar/18 $$\:{find}\:\:\:\:\int_{{a}} ^{{b}} \:\:\:\:\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\sqrt{\mathrm{1}+{x}^{\mathrm{4}} }}{dx}\:\:{with}\:{a}>\mathrm{1}\:{and}\:{b}>\mathrm{1}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com