Question Number 18233 by Joel577 last updated on 17/Jul/17 $$\mathrm{If}\:{y}\:=\:\sqrt{{x}^{\mathrm{2}} \:+\:\sqrt{{x}^{\mathrm{2}} \:+\:\sqrt{{x}^{\mathrm{2}} \:+\:\sqrt{…}}}} \\ $$$$\mathrm{find}\:\int\left({y}\:+\:\sqrt{{y}}\right)\:{dx} \\ $$ Commented by alex041103 last updated on 17/Jul/17 $${did}\:{you}\:{mean}\:{y}=\sqrt{{x}^{\mathrm{2}}…
Question Number 18232 by Joel577 last updated on 17/Jul/17 $$\mathrm{If}\:{f}\left({x}\right)\:=\:\sqrt{{x}^{\mathrm{2}} \sqrt{\mathrm{3}\sqrt{{x}^{\mathrm{2}} \sqrt{\mathrm{3}\sqrt{}…}}}} \\ $$$$\mathrm{find}\:\int\:{f}\left({x}\right)\:{dx} \\ $$ Answered by alex041103 last updated on 17/Jul/17 $${f}\left({x}\right)=\sqrt{{x}^{\mathrm{2}} \sqrt{\mathrm{3}{f}\left({x}\right)}}…
Question Number 83767 by mr W last updated on 05/Mar/20 Commented by mr W last updated on 06/Mar/20 $${Find}\:{the}\:{minimum}\:{of}\:{the}\:{perimeter} \\ $$$${of}\:{triangle}\:{PQR}. \\ $$ Answered by…
Question Number 149296 by mathdanisur last updated on 04/Aug/21 $${if}\:\:\:{a}\:;\:{b}\:>\:\mathrm{0} \\ $$$${find}\:\:\:\left[\:\frac{\left({a}^{\mathrm{2}} \:+\:\mathrm{4}\right)\left({b}^{\mathrm{2}} \:+\:\mathrm{9}\right)}{{ab}}\:\right]_{\boldsymbol{{min}}} =\:? \\ $$ Answered by dumitrel last updated on 04/Aug/21 $$\mathrm{24}\:\left({pentru}\:{a}=\mathrm{2},{b}=\mathrm{3}\right)…
Question Number 18224 by Arnab Maiti last updated on 17/Jul/17 $$\int\mathrm{cos2x}\:\mathrm{ln}\left(\mathrm{1}+\mathrm{tanx}\right)\mathrm{dx} \\ $$ Answered by alex041103 last updated on 17/Jul/17 $${We}\:{integrate}\:{by}\:{parts} \\ $$$${u}={ln}\left(\mathrm{1}+{tan}\:{x}\right)\:\:\:{dv}={cos}\mathrm{2}{x} \\ $$$${du}=\frac{{sec}^{\mathrm{2}}…
Question Number 18223 by Arnab Maiti last updated on 17/Jul/17 $$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\:\pi} \frac{\mathrm{x}\:\mathrm{tanx}}{\mathrm{tanx}+\mathrm{secx}}\mathrm{dx}=\frac{\pi}{\mathrm{2}}\left(\pi−\mathrm{2}\right) \\ $$ Answered by alex041103 last updated on 17/Jul/17 $${First}\:{we}\:{will}\:{integrate}\:{by}\:{parts} \\ $$$${u}={x}\:\:\:\:{dv}=\frac{{tan}\:{x}}{{tan}\:{x}\:+\:{sec}\:{x}}…
Question Number 149292 by mathdanisur last updated on 04/Aug/21 $${if}\:\:\:{sin}\mathrm{2}\boldsymbol{\alpha}\:=\:-\:\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${find}\:\:\:\mathrm{3}{tg}^{\mathrm{2}} \left(\frac{\mathrm{3}\boldsymbol{\pi}}{\mathrm{4}}\:-\:\boldsymbol{\alpha}\right)\:=\:? \\ $$ Answered by Ar Brandon last updated on 04/Aug/21 $$\mathrm{sin2}\alpha=−\frac{\mathrm{1}}{\mathrm{3}} \\…
Question Number 83759 by M±th+et£s last updated on 05/Mar/20 $$\mathrm{3}^{{x}} \:\mathrm{8}^{\frac{{x}}{{x}+\mathrm{2}}} =\mathrm{6} \\ $$ Commented by M±th+et£s last updated on 05/Mar/20 $${solve}\:{the}\:{equation} \\ $$ Commented…
Question Number 18222 by Arnab Maiti last updated on 17/Jul/17 $$\mathrm{show}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \frac{\mathrm{x}\:\mathrm{sinx}}{\mathrm{1}+\mathrm{cos}^{\mathrm{2}} \mathrm{x}}\mathrm{dx}=\frac{\pi}{\mathrm{4}} \\ $$ Commented by Arnab Maiti last updated on 17/Jul/17 $$\mathrm{please}\:\mathrm{help}\:\mathrm{with}\:\mathrm{these}\:\mathrm{questions}.…
Question Number 83756 by naka3546 last updated on 05/Mar/20 $${Find}\:\:{all}\:\:{real}\:\:{solutions}\:\:{of}\:\:\left({x},\:{y}\right)\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:\:\:\:\:{x}\:+\:\mathrm{3}{y}\:+\:\frac{\mathrm{4}}{{x}\:+\:{y}}\:\:=\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:{y}\:+\:\mathrm{3}{x}\:+\:\frac{\mathrm{5}}{{x}\:+\:{y}}\:\:=\:\:\mathrm{7} \\ $$ Commented by Prithwish Sen 1 last updated on 05/Mar/20…