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} \\ $$…
Question Number 36649 by rahul 19 last updated on 03/Jun/18 $$\int\:\frac{\mathrm{1}}{{x}^{\mathrm{4}} +\mathrm{1}}\:{dx} \\ $$ Commented by rahul 19 last updated on 03/Jun/18 $$\int\:\frac{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }}{{x}^{\mathrm{2}} +\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 167716 by cortano1 last updated on 23/Mar/22 Answered by mahdipoor last updated on 23/Mar/22 $$\Rightarrow \\ $$$${f}^{\:'} \left({x}\right)={cosx}+{f}^{\:'} \left({x}\right)\left(\mathrm{2}{sinx}−{sin}^{\mathrm{2}} {x}\right) \\ $$$$\Rightarrow{f}^{\:'} \left({x}\right)=\frac{{cosx}}{\mathrm{1}+{sin}^{\mathrm{2}}…
Question Number 102183 by bemath last updated on 07/Jul/20 $$\int\:\frac{\mathrm{cos}\:\theta}{\mathrm{sin}\:\theta−\mathrm{cos}\:\theta}\:{d}\theta\:? \\ $$ Answered by Dwaipayan Shikari last updated on 07/Jul/20 $$\frac{\mathrm{1}}{\mathrm{2}}{log}\left({sin}\theta−{cos}\theta\right)−\frac{\theta}{\mathrm{2}}+{C} \\ $$$${I}=\int\frac{{cos}\theta}{{sin}\theta−{cos}\theta}{d}\theta \\ $$$${I}=\int\frac{{sin}\theta}{{sin}\theta−{cos}\theta}−\mathrm{1}{d}\theta…
Question Number 36643 by rahul 19 last updated on 03/Jun/18 $$\int\:\frac{{x}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:=\:? \\ $$ Commented by math khazana by abdo last updated on 09/Aug/18…