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 $$\:\:\:{I}\:\:=\:\mathrm{2}\int_{\mathrm{0}} ^{\infty}…
Question Number 171371 by pticantor last updated on 13/Jun/22 $$\int_{−\infty} ^{+\infty} \frac{\boldsymbol{{dx}}}{\mathrm{1}+\boldsymbol{{x}}^{\mathrm{4}} }=? \\ $$ Answered by aleks041103 last updated on 13/Jun/22 $${solve}\:{using}\:{complex}\:{analysis} \\ $$$${we}\:{inregrate}\:{the}\:{complex}\:{function}…
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Question Number 105815 by I want to learn more last updated on 31/Jul/20 Answered by john santu last updated on 01/Aug/20 $$\frac{{dx}}{{d}\theta}\:=\:\mathrm{1}+\mathrm{sin}\:\theta\:;\:\frac{{dy}}{{d}\theta}\:=\:\mathrm{sin}\:\theta \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{2}\pi}…
Question Number 40270 by MJS last updated on 18/Jul/18 $$\mathrm{calculate}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{one}\:“\mathrm{leaf}''\:\mathrm{of} \\ $$$${r}=\mathrm{sin}\:{n}\theta \\ $$$${n}\in\mathbb{N} \\ $$ Answered by MrW3 last updated on 19/Jul/18 $${one}\:{leaf}\:{means}\:\mathrm{0}\leqslant\theta\leqslant\frac{\pi}{{n}} \\…
Question Number 40251 by MJS last updated on 17/Jul/18 $$\mathrm{1}.\:\:\:\:\:\int\frac{{d}\alpha}{\mathrm{sin}\:\mathrm{2}\alpha\:+\mathrm{tan}\:\mathrm{3}\alpha}=? \\ $$$$\mathrm{2}.\:\:\:\:\:\int\frac{{d}\beta}{\mathrm{cos}\:\mathrm{2}\beta\:+\mathrm{cos}\:\mathrm{3}\beta}=? \\ $$$$\mathrm{3}.\:\:\:\:\:\int\frac{{d}\gamma}{\mathrm{sinh}\:\mathrm{2}\gamma\:+\mathrm{tanh}\:\mathrm{3}\gamma}=? \\ $$$$\mathrm{4}.\:\:\:\:\:\int\frac{{d}\delta}{\mathrm{cosh}\:\mathrm{2}\delta\:+\mathrm{cosh}\:\mathrm{3}\delta}=? \\ $$ Answered by maxmathsup by imad last updated…