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 $$\mathrm{cos}\:{y}\left(\frac{{dy}}{{dx}}\right)\:=\:\frac{{x}+\mathrm{sin}\:{y}}{\mathrm{2sin}\:{y}−{x}} \\ $$$${let}\:\:\mathrm{sin}\:{y}={t}…
Question Number 40399 by rahul 19 last updated on 21/Jul/18 $$\mathrm{Solve}\:: \\ $$$$\left(\mathrm{2}\sqrt{{xy}}\:−{x}\right){dy}\:+\:{ydx}\:=\:\mathrm{0}. \\ $$ Answered by rahul 19 last updated on 21/Jul/18 $$\mathrm{ok}\:\mathrm{so},\:\mathrm{i}\:\mathrm{was}\:\mathrm{able}\:\mathrm{to}\:\mathrm{do}\:\mathrm{by}\:\mathrm{taking}\:\frac{\mathrm{y}}{{x}}={t} \\…
Question Number 40380 by rahul 19 last updated on 21/Jul/18 $${S}\mathrm{olve}\::\:\:\:\:\:\frac{\mathrm{dy}}{\mathrm{d}{x}}\:=\:\frac{{x}+{y}}{{x}−{y}} \\ $$ Commented by rahul 19 last updated on 21/Jul/18 $$\mathrm{i}'\:\mathrm{m}\:\mathrm{getting}\: \\ $$$$\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{y}}{{x}}\:=\:{lnx}\:+\:\frac{\mathrm{1}}{\mathrm{2}}{ln}\left(\mathrm{1}+\frac{{y}^{\mathrm{2}}…
Question Number 171442 by mnjuly1970 last updated on 15/Jun/22 Commented by infinityaction last updated on 15/Jun/22 $$\:\:\:\:{e}^{{x}} \left(\mathrm{1}+{x}\right){dx}\:+\:\left({ye}^{{y}} −{xe}^{{x}} \right){dy}\:=\:\mathrm{0} \\ $$$$\:\:\:\:{let}\:\:{t}\:=\:{xe}^{{x}} \\ $$$$\:\:\:\:{e}^{{x}} \left(\mathrm{1}+{x}\right){dx}\:=\:{dt}…
Question Number 171392 by cortano1 last updated on 14/Jun/22 $$\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:\frac{\mathrm{cos}\:{x}}{\left(\mathrm{1}+\sqrt{\mathrm{sin}\:\mathrm{2}{x}}\:\right)^{\mathrm{3}} }\:{dx}\:=? \\ $$ Commented by infinityaction last updated on 19/Jun/22 $$\:\:\:\:\:\:\:{I}\:=\:\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \frac{\mathrm{cos}\:\left(\pi/\mathrm{2}\:−\:{x}\right)}{\mathrm{1}+\sqrt{\mathrm{sin}\:\mathrm{2}\left(\pi/\mathrm{2}\:−{x}\right)}}{dx}…
Question Number 105862 by bemath last updated on 01/Aug/20 $$\int\:\frac{{dx}}{\mathrm{9}+\mathrm{16cos}\:^{\mathrm{2}} {x}}\:? \\ $$ Commented by bemath last updated on 01/Aug/20 $${thank}\:{you} \\ $$ Answered by…
Question Number 40322 by rahul 19 last updated on 19/Jul/18 $$\mathrm{Solve}\:: \\ $$$$\:\frac{\mathrm{d}^{\mathrm{2}} \mathrm{y}}{\mathrm{d}{x}^{\mathrm{2}} }\:=\:\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \\ $$ Commented by rahul 19 last updated on 19/Jul/18…
Question Number 171395 by pticantor last updated on 14/Jun/22 $$\int_{−\infty} ^{+\infty} \frac{\boldsymbol{{x}}^{\mathrm{2}} }{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{4}} }\boldsymbol{{dx}} \\ $$ Commented by infinityaction last updated on 19/Jun/22 $$\:\:\:{I}\:\:=\:\mathrm{2}\int_{\mathrm{0}} ^{\infty}…