Question Number 41514 by maxmathsup by imad last updated on 08/Aug/18 $${find}\:\:\:\int\:\:{cos}\left({lnx}\right){dx}\: \\ $$ Answered by alex041103 last updated on 09/Aug/18 $${We}\:{know}\:{that}\:{cos}\left(\theta\right)={Re}\left({e}^{{i}\theta} \right) \\ $$$${We}\:{will}\:{assume}\:{x}\epsilon\mathbb{R}.…
Question Number 107051 by Ar Brandon last updated on 08/Aug/20 $$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{cosx}}{\mathrm{2}+\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated on 08/Aug/20 $$\int_{\mathrm{0}}…
Question Number 172583 by mathlove last updated on 29/Jun/22 Commented by mr W last updated on 29/Jun/22 $${can}\:{you}\:{explain}\:{what}\:{this}\:{is}? \\ $$ Commented by mr W last…
Question Number 107036 by john santu last updated on 08/Aug/20 $$\int\:\frac{\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\:\mathrm{dx}}{\mathrm{x}^{\mathrm{4}} }\:? \\ $$ Commented by kaivan.ahmadi last updated on 08/Aug/20 $${x}={tgu}\Rightarrow{dx}=\left(\mathrm{1}+{tg}^{\mathrm{2}} {u}\right){du}={sec}^{\mathrm{2}} {udu}…
Question Number 172564 by Mathspace last updated on 28/Jun/22 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}}\sqrt{\mathrm{1}−\sqrt{{x}}}{lnx}\:{dx} \\ $$ Answered by Ar Brandon last updated on 28/Jun/22 $${I}=\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{{x}}\sqrt{\mathrm{1}−\sqrt{{x}}}\mathrm{ln}{xdx},\:{x}={t}^{\mathrm{2}}…
Question Number 41487 by behi83417@gmail.com last updated on 08/Aug/18 Commented by maxmathsup by imad last updated on 08/Aug/18 $$\left.\mathrm{2}\right)\:{we}\:{have}\:{I}\:=\:\int\:\:\:\:\:\:\:\frac{{dx}}{\left(\mathrm{1}+{x}\right)\sqrt{\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}}}\:\:{changement}\:{x}+\frac{\mathrm{1}}{\mathrm{2}}\:=\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{sh}\left({t}\right)\:{give} \\ $$$${I}\:=\:\int\:\:\:\:\:\:\frac{\mathrm{1}}{\left(\mathrm{1}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{sh}\left({t}\right)−\frac{\mathrm{1}}{\mathrm{2}}\right)\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{ch}\left({t}\right)}\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{ch}\left({t}\right){dt} \\ $$$$=\int\:\:\:\:\:\:\:\:\:\:\:\frac{{dt}}{\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}{sh}\left({t}\right)}\:=\:\int\:\:\:\frac{\mathrm{2}{dt}}{\:\sqrt{\mathrm{3}}\frac{{e}^{{t}} −{e}^{−{t}}…
Question Number 172555 by cortano1 last updated on 28/Jun/22 $$\:\:\:\:\:\:\underset{\mathrm{1}/\mathrm{5}} {\overset{\mathrm{5}} {\int}}\:\frac{\mathrm{arctan}\:\left({x}\right)}{{x}}\:{dx}\:=? \\ $$ Commented by greougoury555 last updated on 28/Jun/22 $$\:=\:\mathrm{ln}\:\sqrt{\mathrm{5}^{\pi} }\:=\:\frac{\pi}{\mathrm{2}}\:\mathrm{ln}\:\mathrm{5} \\ $$…
Question Number 107002 by Ar Brandon last updated on 08/Aug/20 $$\int_{\mathrm{0}} ^{\pi} \frac{\mathrm{cosx}}{\:\sqrt{\mathrm{2}−\mathrm{sin}^{\mathrm{2}} \mathrm{x}}}\mathrm{dx} \\ $$ Answered by bemath last updated on 08/Aug/20 $$\underset{\mathrm{0}} {\overset{\pi}…
Question Number 41461 by rahul 19 last updated on 07/Aug/18 $$\mathrm{Find}\:\mathrm{area}\:\mathrm{of}\:\mathrm{square}\:\mathrm{inserted}\:\mathrm{in}\:\mathrm{curve} \\ $$$$\mathrm{f}\left({x}\right)=\:\mathrm{3}{x}−{x}^{\mathrm{3}} . \\ $$ Commented by rahul 19 last updated on 07/Aug/18 Commented…
Question Number 172520 by Mikenice last updated on 28/Jun/22 Commented by mr W last updated on 28/Jun/22 $${x}=\mathrm{3}{W}\left(\mathrm{1}\right)\approx\mathrm{1}.\mathrm{70143} \\ $$$${see}\:{Q}#\:\mathrm{172510} \\ $$ Terms of Service…