Question Number 106010 by bemath last updated on 02/Aug/20 $$\int\:\frac{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}\:{dx}\: \\ $$ Answered by Dwaipayan Shikari last updated on 02/Aug/20 $$\int\frac{\mathrm{1}+{x}}{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}+\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}}…
Question Number 40467 by gunawan last updated on 22/Jul/18 $$\int\mathrm{ln}\:\mid\sqrt{{x}+\mathrm{1}}+\sqrt{{x}}\mid\:{dx}= \\ $$ Commented by maxmathsup by imad last updated on 22/Jul/18 $${let}\:{I}\:=\:\int\:{ln}\mid\sqrt{{x}+\mathrm{1}}\:+\sqrt{{x}}\mid{dx}\:\:{due}\:{to}\:{x}\geqslant\mathrm{0}\:{we}\:{have} \\ $$$${I}\:=\:\int\:{ln}\left(\sqrt{{x}+\mathrm{1}}+\sqrt{{x}}\right){dx}\:=_{\sqrt{{x}}={t}} \:\mathrm{2}\:\:\int{ln}\left(\sqrt{\mathrm{1}+{t}^{\mathrm{2}}…
Question Number 106001 by Algoritm last updated on 02/Aug/20 Answered by JDamian last updated on 02/Aug/20 $$\mathrm{5056}\left({e}−\mathrm{1}\right) \\ $$ Answered by mr W last updated…
Question Number 105983 by bemath last updated on 02/Aug/20 $$\int\:\frac{\mathrm{sin}\:{x}\:{dx}}{\mathrm{6}−\mathrm{sin}\:^{\mathrm{2}} {x}}\:?\:\: \\ $$ Commented by bemath last updated on 02/Aug/20 $$\int\:\frac{\mathrm{sin}\:{x}}{\mathrm{6}−\left(\mathrm{1}−\mathrm{cos}\:^{\mathrm{2}} {x}\right)}\:{dx}\:=\:−\int\frac{{d}\left(\mathrm{cos}\:{x}\right)}{\mathrm{5}+\mathrm{cos}\:^{\mathrm{2}} {x}} \\ $$$${let}\:\flat\:=\:\mathrm{cos}\:{x}…
Question Number 40442 by rahul 19 last updated on 21/Jul/18 $$\mathrm{Solve}\:: \\ $$$$\mathrm{y}^{\mathrm{4}} \mathrm{d}{x}\:+\:\mathrm{2}{x}\mathrm{y}^{\mathrm{3}} \mathrm{dy}\:=\:\frac{\mathrm{yd}{x}−\:{x}\mathrm{dy}}{{x}^{\mathrm{3}} \mathrm{y}^{\mathrm{3}} }. \\ $$ Answered by ajfour last updated on…
Question Number 105969 by Ar Brandon last updated on 02/Aug/20 $$\int\frac{\mathrm{sinx}+\mathrm{cosx}}{\:\sqrt{\mathrm{1}+\mathrm{sin2x}}}\mathrm{dx} \\ $$ Answered by bobhans last updated on 02/Aug/20 $$\int\:\frac{\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} }}\:\mathrm{dx}\:=\:\int\frac{\:\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)\mathrm{dx}}{\mid\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\mid} \\ $$$$=\:\pm\:\int\:\mathrm{dx}\:=\:\pm\mathrm{x}\:+\:\mathrm{C} \\…
Question Number 40422 by rahul 19 last updated on 21/Jul/18 $$\mathrm{Solve}: \\ $$$$\mathrm{yd}{x}\:−\:{xdy}\:+\mathrm{log}\:{xdx}\:=\mathrm{0} \\ $$ Commented by prof Abdo imad last updated on 22/Jul/18 $$\Rightarrow{y}\:\:−{x}\frac{{dy}}{{dx}}\:+{ln}\left({x}\right)=\mathrm{0}\:\Rightarrow{xy}^{'}…
Question Number 105951 by Study last updated on 01/Aug/20 Answered by Dwaipayan Shikari last updated on 01/Aug/20 $$\sqrt{\frac{{x}}{\:\sqrt{\frac{{x}}{\frac{{x}}{}…}}}}={p} \\ $$$$\sqrt{\frac{{x}}{{p}}}={p} \\ $$$${p}=\sqrt[{\mathrm{3}}]{{x}} \\ $$$$\int{pdx}=\int{x}^{\frac{\mathrm{1}}{\mathrm{3}}} {dx}=\frac{\mathrm{3}}{\mathrm{4}}{x}^{\frac{\mathrm{4}}{\mathrm{3}}}…
Question Number 105940 by Dwaipayan Shikari last updated on 01/Aug/20 $$\int_{\mathrm{0}} ^{\mathrm{1}} {log}\left({tan}\theta\right){d}\theta \\ $$ Answered by mathmax by abdo last updated on 01/Aug/20 $$\mathrm{A}\:=\int_{\mathrm{0}}…
Question Number 40397 by rahul 19 last updated on 21/Jul/18 $$\mathrm{Solve}\:: \\ $$$$\frac{\mathrm{dy}}{{dx}}\:=\:\frac{\mathrm{sin}\:{y}\:+\:{x}}{\mathrm{sin}\:\mathrm{2}{y}\:−\:{x}\mathrm{cos}\:{y}}\:. \\ $$ Answered by ajfour last updated on 21/Jul/18 $$\mathrm{cos}\:{y}\left(\frac{{dy}}{{dx}}\right)\:=\:\frac{{x}+\mathrm{sin}\:{y}}{\mathrm{2sin}\:{y}−{x}} \\ $$$${let}\:\:\mathrm{sin}\:{y}={t}…