Question Number 124334 by Ar Brandon last updated on 02/Dec/20 $$\int\sqrt{\frac{\mathrm{cos}{x}−\mathrm{cos}^{\mathrm{3}} {x}}{\left(\mathrm{1}−\mathrm{cos}^{\mathrm{3}} {x}\right)}}\mathrm{d}{x} \\ $$ Answered by MJS_new last updated on 02/Dec/20 $$=\int\frac{\mathrm{sin}\:{x}\:\sqrt{\mathrm{cos}\:{x}}}{\:\sqrt{\mathrm{1}−\mathrm{cos}^{\mathrm{3}} \:{x}}}{dx}= \\…
Question Number 58791 by Tawa1 last updated on 30/Apr/19 $$\:\boldsymbol{\mathrm{Show}}\:\boldsymbol{\mathrm{that}}:\:\:\:\:\:\:\:\:\:\int_{\:\mathrm{0}} ^{\:\infty} \:\:\:\frac{\boldsymbol{\mathrm{sin}}\left(\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}}\:\:\:=\:\:\frac{\pi}{\mathrm{2}} \\ $$ Answered by tanmay last updated on 30/Apr/19 $${it}\:{has}\:{some}\:{trick}\:{to}\:{solve}… \\ $$$${F}\left({a}\right)=\int_{\mathrm{0}} ^{\infty}…
Question Number 58774 by maxmathsup by imad last updated on 29/Apr/19 $${let}\:{f}\left({x}\right)\:=\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{d}\theta}{\mathrm{1}+{xtan}\theta}\:\:\:{with}\:{x}\:{real} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{also}\:{g}\left({x}\right)\:=\int_{\frac{\pi}{\mathrm{3}}} ^{\frac{\pi}{\mathrm{2}}} \:\:\:\frac{{tan}\theta}{\left(\mathrm{1}+{xtan}\theta\right)^{\mathrm{2}} }\:{d}\theta \\ $$$$\left.\mathrm{3}\right)\:{let}\:{U}_{{n}} \left({x}\right)\:={f}^{\left({n}\right)} \left({x}\right)\:\:{give}\:{U}_{{n}}…
Question Number 58770 by Mr X pcx last updated on 29/Apr/19 $${find}\:{the}\:{value}\:{of}\:{integrals} \\ $$$$\:{I}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }\:\:\:,\:{J}\:=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{5}} } \\ $$ Commented…
Question Number 189825 by TUN last updated on 22/Mar/23 $$\underset{{a}} {\int}^{{b}} \sqrt{\left({x}−{a}\right)\left({b}−{x}\right)}=¿ \\ $$ Answered by Frix last updated on 14/Apr/23 $$\mathrm{circle}: \\ $$$$\left({x}−\frac{{a}+{b}}{\mathrm{2}}\right)^{\mathrm{2}} +{y}^{\mathrm{2}}…
Question Number 124261 by Ar Brandon last updated on 02/Dec/20 $$\int\frac{\mathrm{2x}^{\mathrm{2}} +\mathrm{5x}+\mathrm{9}}{\left(\mathrm{x}+\mathrm{1}\right)\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}}\mathrm{dx} \\ $$ Commented by MJS_new last updated on 02/Dec/20 $$\mathrm{I}\:\mathrm{think}\:\mathrm{something}\:\mathrm{went}\:\mathrm{wrong}… \\ $$…
Question Number 124252 by bramlexs22 last updated on 02/Dec/20 $$\:\:{o}\left({x}\right)=\int\:\frac{{dx}}{\mathrm{sec}\:^{\mathrm{3}} {x}\:\mathrm{sin}\:^{\mathrm{4}} {x}}\: \\ $$ Answered by Dwaipayan Shikari last updated on 02/Dec/20 $$\int\frac{{cos}^{\mathrm{3}} {x}}{{sin}^{\mathrm{4}} {x}}{dx}=\int\frac{{cosx}\left(\mathrm{1}−{sin}^{\mathrm{2}}…
Question Number 58717 by rahul 19 last updated on 28/Apr/19 Commented by rahul 19 last updated on 28/Apr/19 $${Curve}\:{is}\:{y}={e}^{−{x}^{\mathrm{2}} } . \\ $$$${Ans}:{a},{b},{d}. \\ $$…
Question Number 124251 by bramlexs22 last updated on 02/Dec/20 $$\:\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{{x}^{\mathrm{2}} }{\mathrm{cosh}\:{x}}\:{dx}\:? \\ $$ Commented by Dwaipayan Shikari last updated on 02/Dec/20 $$\mathrm{2}\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 124228 by mnjuly1970 last updated on 01/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…:::\:\:{nice}\:\:{calculus}:::… \\ $$$$\:\:\:\:\:\:{evaluate} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left({ln}\left({x}\right)\right)}{\mathrm{1}+{x}^{\mathrm{3}} }{dx}=….??? \\ $$ Answered by Lordose last updated on…