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 $$\mathrm{I}=\int_{\frac{\mathrm{1}}{\mathrm{a}}} ^{\mathrm{a}}…
Question Number 144142 by bobhans last updated on 22/Jun/21 $$\:\int\:\frac{\sqrt{\mathrm{cos}\:\mathrm{x}+\sqrt{\mathrm{cos}\:\mathrm{x}+\sqrt{\mathrm{cos}\:\mathrm{x}+\sqrt{\mathrm{cos}\:\mathrm{x}+\sqrt{…}}}}}}{\mathrm{sin}\:\mathrm{x}}\:\mathrm{dx} \\ $$ Answered by liberty last updated on 22/Jun/21 $$\sqrt{\mathrm{cos}\:\mathrm{x}+\sqrt{\mathrm{cos}\:\mathrm{x}+\sqrt{\mathrm{cos}\:\mathrm{x}+\sqrt{…}}}}\:=\:\ell\: \\ $$$$\sqrt{\mathrm{cos}\:\mathrm{x}+\ell}\:=\:\ell\:\Rightarrow\ell^{\mathrm{2}} −\ell−\mathrm{cos}\:\mathrm{x}\:=\mathrm{0} \\ $$$$\Rightarrow\ell\:=\:\frac{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{4cos}\:\mathrm{x}}}{\mathrm{2}}…
Question Number 144116 by BHOOPENDRA last updated on 21/Jun/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 78575 by TawaTawa last updated on 18/Jan/20 $$\int\:\sqrt{\mathrm{tan}\:\mathrm{x}}\:\:\mathrm{dx} \\ $$ Answered by peter frank last updated on 18/Jan/20 $${u}=\sqrt{\mathrm{tan}\:{x}} \\ $$$${dx}=\frac{\mathrm{2}{udu}}{\mathrm{1}+{u}^{\mathrm{4}} } \\…