Question Number 54971 by peter frank last updated on 15/Feb/19 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\sqrt{{tanx}}\:\mathrm{sin}\:^{\mathrm{2}} {x}}{\:\sqrt{\mathrm{sin}\:{x}\mathrm{cos}\:{x}}\:\mathrm{tan}\:{x}}{dx} \\ $$ Answered by kaivan.ahmadi last updated on 15/Feb/19 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…
Question Number 54936 by maxmathsup by imad last updated on 14/Feb/19 $${let}\:{f}\left(\theta\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}\left({cos}\theta\right){x}\:+\mathrm{1}}{dx}\:\:\:{with}\:\theta\:\in\:{R}\:. \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}\left(\theta\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:{g}\left(\theta\right)=\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{xsin}\theta}{\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}{cos}\theta\:{x}\:+\mathrm{1}}}{dx} \\ $$ Commented…
Question Number 54919 by maxmathsup by imad last updated on 14/Feb/19 $${calculate}\:\int_{\mathrm{1}} ^{\sqrt{\mathrm{2}}} \left({x}^{\mathrm{3}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −\mathrm{1}}{dx} \\ $$ Commented by Abdo msup. last updated on…
Question Number 185985 by cortano1 last updated on 30/Jan/23 $$\:\:\:\int\:\frac{{dx}}{\:\sqrt{\mathrm{sin}\:{x}\left(\mathrm{1}+\mathrm{cos}\:{x}\right)}}\:=? \\ $$ Answered by ARUNG_Brandon_MBU last updated on 30/Jan/23 $${I}=\int\frac{{dx}}{\:\sqrt{\mathrm{sin}{x}\left(\mathrm{1}+\mathrm{cos}{x}\right)}}=\int\frac{{dx}}{\mathrm{2}\sqrt{\mathrm{sin}\frac{{x}}{\mathrm{2}}\mathrm{cos}^{\mathrm{3}} \frac{{x}}{\mathrm{2}}}} \\ $$$$\:\:=\int\frac{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{sec}^{\mathrm{2}} \frac{{x}}{\mathrm{2}}}{\:\sqrt{\mathrm{tan}\frac{{x}}{\mathrm{2}}}}{dx}=\int\frac{{d}\left(\mathrm{tan}\frac{{x}}{\mathrm{2}}\right)}{\:\sqrt{\mathrm{tan}\frac{{x}}{\mathrm{2}}}}=\mathrm{2}\sqrt{\mathrm{tan}\frac{{x}}{\mathrm{2}}}+{C} \\…
Question Number 120438 by bramlexs22 last updated on 31/Oct/20 Answered by TANMAY PANACEA last updated on 31/Oct/20 $${formula} \\ $$$$\int_{{a}} ^{{b}} {f}\left({x}\right){dx}=\int_{\mathrm{0}} ^{{b}} {f}\left({a}+{b}−{x}\right){dx} \\…
Question Number 54896 by yusufbode1996 last updated on 14/Feb/19 $$\int\sqrt{}\left({x}\mathrm{2}+\mathrm{2}{x}+\mathrm{2}\right) \\ $$ Commented by maxmathsup by imad last updated on 14/Feb/19 $${let}\:{I}\:=\int\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{2}{x}+\mathrm{2}}{dx}\:\Rightarrow{I}\:=\int\:\sqrt{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \:+\mathrm{1}}{dx}\:\:{changement}\:{x}+\mathrm{1}\:={sh}\left({t}\right)\:{give} \\…
Question Number 185961 by Michaelfaraday last updated on 30/Jan/23 $${solve}: \\ $$$$\int\sqrt{\left[{x}^{\mathrm{2}} −\mathrm{1}\right]\:{dx}} \\ $$ Answered by Frix last updated on 30/Jan/23 $$\mathrm{No}\:\mathrm{indefinite}\:\mathrm{integral}\:\mathrm{exists}. \\ $$…
Question Number 185959 by Michaelfaraday last updated on 30/Jan/23 $${solve}: \\ $$$$\int{x}^{{Inx}} {dx} \\ $$ Answered by Frix last updated on 30/Jan/23 $$\int{x}^{\mathrm{ln}\:{x}} {dx}\:\overset{{t}=\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{ln}\:{x}} {=}\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{\mathrm{e}}}\int\mathrm{e}^{{t}^{\mathrm{2}}…
Question Number 185944 by Michaelfaraday last updated on 30/Jan/23 Commented by mr W last updated on 30/Jan/23 $${this}\:{app}\:{is}\:{developed}\:{for}\:{writting} \\ $$$${mathematical}\:{formulas}.\:{is}\:{it}\:{not} \\ $$$${easier}\:{and}\:{better}\:{for}\:{you}\:{to}\:{write} \\ $$$$\int{x}^{\mathrm{3}} \:\mathrm{ln}\:\left({x}+\mathrm{4}\right)\:{dx}\:{instead}\:{of}\:…
Question Number 185935 by cortano1 last updated on 30/Jan/23 $$\:\:\:\int\:\frac{\mathrm{1}−\mathrm{cos}\:{x}}{\left(\mathrm{1}+\mathrm{cos}\:{x}\right)\:\mathrm{cos}\:{x}}\:{dx}\:=? \\ $$ Answered by Ar Brandon last updated on 30/Jan/23 $${I}=\int\frac{\mathrm{1}−\mathrm{cos}{x}}{\left(\mathrm{1}+\mathrm{cos}{x}\right)\mathrm{cos}{x}}{dx}=\int\frac{\left(\mathrm{1}−\mathrm{cos}{x}\right)^{\mathrm{2}} }{\left(\mathrm{1}−\mathrm{cos}^{\mathrm{2}} {x}\right)\mathrm{cos}{x}}{dx} \\ $$$$\:\:=\int\frac{\mathrm{1}−\mathrm{2cos}{x}+\mathrm{cos}^{\mathrm{2}}…