Question Number 109378 by shahria14 last updated on 23/Aug/20 Answered by john santu last updated on 23/Aug/20 $$\:\:\:\:\:\frac{\approx{JS}\:\approx}{\blacksquare\bigstar\blacksquare} \\ $$$$\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}.\frac{\mathrm{1}+{x}}{\mathrm{1}+{x}}}\:=\:\frac{\mathrm{1}+{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\: \\ $$$$\int\:\sqrt{\frac{\mathrm{1}+{x}}{\mathrm{1}−{x}}}\:{dx}\:=\:\int\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx}\:+\int\:\frac{{x}}{\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}\:{dx}…
Question Number 43840 by peter frank last updated on 16/Sep/18 Commented by maxmathsup by imad last updated on 16/Sep/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{sin}^{\mathrm{4}} {x}}{{cos}^{\mathrm{4}} {x}\:+{sin}^{\mathrm{4}} {x}}{dx}\:\:{and}\:{J}\:=\:\int_{\mathrm{0}}…
Question Number 109366 by mnjuly1970 last updated on 23/Aug/20 Commented by 150505R last updated on 24/Aug/20 $${answer}\:{is}\:−\frac{\pi}{\mathrm{8}}{log}\mathrm{2}\:\:…….{small}\:{mistake}\:…. \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 43832 by physics last updated on 16/Sep/18 Commented by physics last updated on 16/Sep/18 $${do}\:{with}\:{full}\:{explanation}\:{please} \\ $$ Commented by maxmathsup by imad last…
Question Number 174896 by amin96 last updated on 14/Aug/22 $$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\int_{−\infty} ^{\:\infty} \frac{\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{csch}}\left(\frac{\boldsymbol{\mathrm{x}}}{\mathrm{2}}\right)}{\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\pi^{\mathrm{2}} }\boldsymbol{\mathrm{dx}}=\pi−\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 43823 by abdo.msup.com last updated on 15/Sep/18 $${let}\:\varphi\left({a},{x}\right)\:=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{dt}}{{x}+{asin}^{\mathrm{2}} {t}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{exlicite}\:{form}\:{of}\:\varphi\left({a},{x}\right) \\ $$$$\left.\mathrm{3}\right){determine}\:\varphi\left(\mathrm{1},{x}\right){and}\:\varphi\left({a},\mathrm{1}\right) \\ $$$$\left.\mathrm{4}\right){find}\:{the}\:{vslue}\:{of}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{dt}}{\mathrm{2}+\mathrm{3}{sin}^{\mathrm{2}} {t}} \\ $$$$\left.\mathrm{5}\right){find}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 43808 by maxmathsup by imad last updated on 15/Sep/18 $${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{{x}^{\mathrm{4}} −{i}}\:{and}\:{J}\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{{x}^{\mathrm{4}} \:+{i}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:\:{values}\:{of}\:{I}\:{and}\:{J} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{I}\:+{J} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty}…
Question Number 43809 by maxmathsup by imad last updated on 15/Sep/18 $${let}\:{f}\left({x}\right)\:=\frac{\mathrm{1}−\sqrt{{x}−\mathrm{1}}}{\mathrm{2}+\sqrt{{x}−\mathrm{1}}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int\:{f}\left({x}\right){dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\:\int\:\:{f}^{−\mathrm{1}} \left({x}\right){dx} \\ $$$$\left.\mathrm{4}\right)\:{find}\:\int\:\:\:\frac{{dx}}{{f}^{−\mathrm{1}} \left({x}\right)}\:. \\ $$…
Question Number 109342 by 150505R last updated on 22/Aug/20 Commented by maths mind last updated on 23/Aug/20 $${x}={tg}\left({t}\right),{dx}=\left(\mathrm{1}+{tg}^{\mathrm{2}} \left({t}\right)\right){dt} \\ $$$$=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} {ln}\left(\frac{{cos}^{\mathrm{2}} \left({t}\right)−{sin}^{\mathrm{2}} \left({t}\right)}{{sin}\left({t}\right){cos}\left({t}\right)}\right).{dt}…
Question Number 109343 by 150505R last updated on 22/Aug/20 Commented by 150505R last updated on 22/Aug/20 $${please}\:{solve} \\ $$ Answered by mathmax by abdo last…