Question Number 144231 by mnjuly1970 last updated on 23/Jun/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{Nice}\:…{Calculus} \\ $$$$\:\:\:\:\:\:{if}\:\:::\:\: \\ $$$$\:\:\:\:\:\:\:\varphi\:\left(\:{n}\:\right)\::=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{x}^{\:{n}} }{\mathrm{1}\:+\:{x}}\:{dx} \\ $$$$\:\:\:\:\:{then}\:\:::\:\:\:\underset{{n}=\mathrm{1}} {\overset{\:\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \:\varphi\:\left({n}\:\right)}{{n}}\:=? \\ $$$$\:\:\:\:\:\:\:…….. \\…
Question Number 78655 by Pratah last updated on 19/Jan/20 Commented by mr W last updated on 19/Jan/20 $$={e}^{{e}^{…^{{e}^{{e}} } } } −{e}^{{e}^{…^{{e}} } } \\…
Question Number 144187 by ArielVyny last updated on 22/Jun/21 $$\int_{\mathrm{0}} ^{+\infty} \frac{{u}^{\mathrm{2}} }{{u}^{\mathrm{8}} +\mathrm{2}{u}^{\mathrm{4}} +\mathrm{1}}{du} \\ $$ Answered by Ar Brandon last updated on 22/Jun/21…
Question Number 144186 by cherokeesay last updated on 22/Jun/21 $${Estimate}\:\int_{\mathrm{0}} ^{\mathrm{0}.\mathrm{5}} \sqrt{\mathrm{1}+{x}^{\mathrm{4}} }\:{dx} \\ $$$${with}\:{an}\:{error}\:\mathrm{0}.\mathrm{0001} \\ $$ Answered by Dwaipayan Shikari last updated on 23/Jun/21…
Question Number 144168 by bekzodjumayev last updated on 22/Jun/21 Answered by Olaf_Thorendsen last updated on 22/Jun/21 $$\mathrm{F}\left({x}\right)\:=\:\int\frac{{dx}}{\mathrm{arccos}{x}} \\ $$$$\mathrm{Let}\:{x}\:=\:\mathrm{cos}\theta \\ $$$$\mathrm{F}\left({x}\right)\:=\:−\int\frac{\mathrm{sin}\theta}{\theta}\:{d}\theta\:=\:−\mathrm{Si}\left(\theta\right)+\mathrm{C} \\ $$$$\mathrm{F}\left({x}\right)\:=\:−\mathrm{Si}\left(\mathrm{arccos}{x}\right)+\mathrm{C} \\ $$…
Question Number 78624 by mathmax by abdo last updated on 19/Jan/20 $${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {e}^{−\mathrm{2}{x}} {ln}\left(\mathrm{1}+{cosx}\right){dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78627 by mathmax by abdo last updated on 19/Jan/20 $${explicite}\:{f}\left({x}\right)=\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({xt}\:+\mathrm{1}\right)}{{t}^{\mathrm{2}} \:+{x}^{\mathrm{2}} }{dt}\:\:{with}\:{x}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78625 by mathmax by abdo last updated on 19/Jan/20 $${calculate}\:\:\int_{−\infty} ^{+\infty} \:\frac{{arctan}\left({x}^{\mathrm{2}} −\mathrm{3}\right)}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by mathmax by abdo last…
Question Number 78621 by mathmax by abdo last updated on 19/Jan/20 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\:\:\int_{{x}} ^{{x}^{\mathrm{3}} } \:\:\frac{{sh}\left({xt}^{\mathrm{2}} \right)}{{sin}\left({xt}\right)}{dt} \\ $$ Commented by mathmax by abdo last…
Question Number 144143 by ArielVyny last updated on 22/Jun/21 $$\int_{\frac{\mathrm{1}}{{a}}} ^{{a}} \frac{{arctg}\left({x}\right)}{{x}}{dx}=??? \\ $$ Answered by mathmax by abdo last updated on 22/Jun/21 $$\mathrm{I}=\int_{\frac{\mathrm{1}}{\mathrm{a}}} ^{\mathrm{a}}…