Question Number 36738 by MJS last updated on 04/Jun/18 $$\left(\mathrm{1}\right)\:\:\:\:\:\int\frac{{d}\alpha}{\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}\alpha\right)^{\mathrm{2}} }= \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\int\frac{{d}\beta}{\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}\beta\right)^{\mathrm{2}} }= \\ $$$$\left(\mathrm{3}\right)\:\:\:\:\:\int\frac{{d}\gamma}{\left(\mathrm{1}+\mathrm{sin}\:\mathrm{2}\gamma\right)\left(\mathrm{1}+\mathrm{cos}\:\mathrm{2}\gamma\right)}= \\ $$ Commented by behi83417@gmail.com last updated on 05/Jun/18…
Question Number 36736 by abdo mathsup 649 cc last updated on 04/Jun/18 $${let}\:\:{f}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{1}−{e}^{{i}\theta} {x}\right){dx} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left(\theta\right) \\ $$ Commented by prof Abdo imad…
Question Number 36728 by a1bgt3@gmail.com last updated on 04/Jun/18 $${the}\:{improper}\:{integral}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{converges}\:{to} \\ $$ Commented by abdo.msup.com last updated on 05/Jun/18 $${I}\:={lim}_{\xi\rightarrow\mathrm{0}} \:\int_{\xi} ^{\mathrm{1}}…
Question Number 102233 by nimnim last updated on 07/Jul/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{under}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\sqrt{\mathrm{a}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} } \\ $$$$\mathrm{included}\:\mathrm{between}\:\mathrm{the}\:\mathrm{lines}\:\mathrm{x}=\mathrm{0}\:\mathrm{and}\:\mathrm{x}=\mathrm{4} \\ $$$$ \\ $$$$\mathrm{plz}\:\mathrm{help}….. \\ $$ Answered by 30-04-1945 last updated…
Question Number 36689 by prof Abdo imad last updated on 04/Jun/18 $$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{3}} \right){dx}\:{then} \\ $$$${find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right){dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{x}^{\mathrm{3}} \right){dx}\:{then}\:…
Question Number 36690 by prof Abdo imad last updated on 04/Jun/18 $${let}\:\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{ln}\left(\mathrm{1}\:−{tx}^{\mathrm{3}} \right){dx}\:\:{with}\:\mathrm{0}<{t}\leqslant\mathrm{1} \\ $$$${find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right)\: \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{ln}\left(\mathrm{2}−{x}^{\mathrm{3}} \right){dx}\:. \\ $$ Commented…
Question Number 36677 by mondodotto@gmail.com last updated on 04/Jun/18 Commented by prof Abdo imad last updated on 04/Jun/18 $$\left.\mathrm{3}\right)\:{let}\:{decompose}\:{F}\left({x}\right)=\:\frac{\mathrm{2}{x}^{\mathrm{3}} \:−\mathrm{4}{x}\:−\mathrm{8}}{\left({x}^{\mathrm{2}} −{x}\right)\left({x}^{\mathrm{2}} \:+\mathrm{4}\right)} \\ $$$${F}\left({x}\right)=\:\frac{\mathrm{2}{x}^{\mathrm{3}} −\mathrm{4}{x}\:−\mathrm{8}}{{x}\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}}…
Question Number 102198 by Study last updated on 07/Jul/20 $$\int\frac{{x}}{{sin}^{\mathrm{2}} {x}−\mathrm{3}}{dx}=? \\ $$ Answered by mathmax by abdo last updated on 08/Jul/20 $$\mathrm{not}\:\mathrm{resoluble}\sqrt{!} \\ $$…
Question Number 102195 by Study last updated on 07/Jul/20 $$\int{sinx}\:{d}\left({sinx}\right)=? \\ $$ Answered by Ar Brandon last updated on 07/Jul/20 $$\frac{\mathrm{sin}^{\mathrm{2}} \mathrm{x}}{\mathrm{2}}+\mathcal{C} \\ $$ Commented…
Question Number 36659 by rahul 19 last updated on 03/Jun/18 $$\int\:\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{4}} {x}+\mathrm{cos}\:^{\mathrm{4}} {x}}\:{dx} \\ $$ Commented by MJS last updated on 03/Jun/18 $$\mathrm{see}\:\mathrm{my}\:\mathrm{answers}\:\mathrm{to}\:\mathrm{Qu}.\:\mathrm{36428} \\ $$…