Question Number 143808 by mnjuly1970 last updated on 18/Jun/21 Answered by Dwaipayan Shikari last updated on 18/Jun/21 $$\xi\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{\left(\mathrm{1}+{x}^{{a}} \right)^{{a}} }{dx} \\ $$$$=\frac{\mathrm{1}}{{a}}\int_{\mathrm{0}} ^{\infty}…
Question Number 143811 by liberty last updated on 18/Jun/21 $$\:\begin{cases}{\mathrm{5}\left(\mathrm{log}\:_{\mathrm{y}} \left(\mathrm{x}\right)+\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{y}\right)\right)=\mathrm{26}}\\{\:\mathrm{xy}\:=\:\mathrm{64}}\end{cases}\mathrm{then} \\ $$$$\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{xy}\:=? \\ $$ Answered by liberty last updated on 18/Jun/21…
Question Number 143810 by Jamshidbek last updated on 18/Jun/21 $$\:\:\:\:\int\mathrm{cos}\left(\mathrm{cosx}\right)\mathrm{dx}=? \\ $$ Answered by mathmax by abdo last updated on 18/Jun/21 $$\int\:\mathrm{cos}\left(\mathrm{cosx}\right)\mathrm{dx}\:=\int\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} \:\mathrm{cos}^{\mathrm{2n}}…
Question Number 78273 by msup trace by abdo last updated on 15/Jan/20 $${let}\:{f}\left(\theta\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dx}}{\mathrm{1}+{sin}\theta\:{sinx}} \\ $$$$ \\ $$$${with}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$$$\left.\mathrm{1}\right)\:{explicite}\:{f}\left(\theta\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{dx}}{\left(\mathrm{1}+{sin}\theta\:{sinx}\right)^{\mathrm{2}}…
Question Number 78270 by msup trace by abdo last updated on 15/Jan/20 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){ln}\left({x}\right)}{{x}^{\mathrm{2}} }{dx} \\ $$$${prove}\:{first}\:{the}\:{convergence}. \\ $$ Commented by mathmax by…
Question Number 78271 by msup trace by abdo last updated on 15/Jan/20 $${calculate}\:{A}_{\theta} \:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dx}}{\mathrm{2}+{cos}\theta\:{sinx}} \\ $$$$−\pi<\theta<\pi \\ $$ Commented by mathmax by abdo…
Question Number 78269 by msup trace by abdo last updated on 15/Jan/20 $${let}\:{f}\left({a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left({ax}\right)}{{x}^{\mathrm{2}} +{a}^{\mathrm{2}} }{dx}\:{with} \\ $$$${a}>\mathrm{0}\:\:{find}\:\:\:\int_{\mathrm{1}} ^{\mathrm{2}} {f}\left({a}\right){da} \\ $$ Commented by…
Question Number 12732 by Joel577 last updated on 30/Apr/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}}\:−\:{x}}{\:\sqrt{{x}}\:+\:{x}} \\ $$ Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17 $$=\mathrm{1} \\ $$ Commented by…
Question Number 78266 by msup trace by abdo last updated on 15/Jan/20 $${calculate}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{ax}^{\mathrm{3}} \right){dx} \\ $$$${with}\:\mathrm{0}<{a}<\mathrm{1} \\ $$ Commented by mathmax by abdo…
Question Number 78267 by msup trace by abdo last updated on 15/Jan/20 $${find}\:\:\int_{−\infty} ^{+\infty} \:\frac{{x}^{\mathrm{2}} −{x}}{{x}^{\mathrm{4}} −{x}^{\mathrm{2}} \:+\mathrm{3}}{dx} \\ $$ Commented by mathmax by abdo…