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…
Question Number 105781 by IE last updated on 31/Jul/20 $$\mathrm{Please},\:\mathrm{I}\:\mathrm{need}\:\mathrm{help}. \\ $$$$\mathrm{Exercise} \\ $$$$\mathrm{We}\:\mathrm{have}\:: \\ $$$$\mathrm{J}_{\mathrm{n}} =\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{4}}} \mathrm{tan}^{\mathrm{n}} \left(\mathrm{x}\right)\:\mathrm{dx} \\ $$$$ \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Establish}\:\mathrm{a}\:\mathrm{recurrence}\:\mathrm{relation} \\…
Question Number 171301 by mpakhrur last updated on 12/Jun/22 $$\int_{\mathrm{1}} ^{\mathrm{2}} \mathrm{6}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3} \\ $$ Commented by Kalebwizeman last updated on 12/Jun/22 $$\left.\frac{\mathrm{6}{x}^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{2}{x}^{\mathrm{2}} }{\mathrm{2}}+\mathrm{3}{x}\right]\underset{\mathrm{1}}…
Question Number 105755 by bemath last updated on 31/Jul/20 $$\int\:\frac{{dx}}{\:\sqrt{{x}\sqrt{{x}}\:−{x}^{\mathrm{2}} }}\:? \\ $$ Answered by john santu last updated on 31/Jul/20 $${let}\:{u}\:=\:\sqrt{{x}}\:\Rightarrow\:\int\:\frac{\mathrm{2}{u}\:{du}}{\:\sqrt{{u}^{\mathrm{3}} −{u}^{\mathrm{4}} }}\:=\: \\…
Question Number 105753 by bramlex last updated on 31/Jul/20 $$\int\:\frac{{x}^{\mathrm{2}} +\mathrm{sin}\:^{\mathrm{2}} {x}}{{x}^{\mathrm{2}} +\mathrm{cos}\:^{\mathrm{2}} {x}}\:{dx}\: \\ $$ Commented by Ar Brandon last updated on 31/Jul/20 $$\mathrm{No}\:\mathrm{limits}\:?…
Question Number 105743 by Skabetix last updated on 31/Jul/20 Commented by Skabetix last updated on 31/Jul/20 $${thank}\:{you}\:{in}\:{advance} \\ $$ Answered by john santu last updated…