Question Number 61041 by mathsolverby Abdo last updated on 28/May/19 $${calculate}\:\int_{\mathrm{1}} ^{+\infty} \:\frac{\left[\mathrm{2}{x}\right]−\left[{x}\right]}{{x}^{\mathrm{4}} }\:{dx}\: \\ $$ Commented by maxmathsup by imad last updated on 29/May/19…
Question Number 61039 by mathsolverby Abdo last updated on 28/May/19 $${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{arctan}\left(\frac{\mathrm{2}}{\mathrm{1}+{x}}\right){dx} \\ $$ Commented by maxmathsup by imad last updated on 29/May/19 $${let}\:{A}\:=\int_{\mathrm{0}}…
Question Number 126571 by benjo_mathlover last updated on 22/Dec/20 $$\:\:\int\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\:\sqrt{\mathrm{tan}\:^{\mathrm{2}} {x}−\mathrm{1}}}\:{dx}\:?\: \\ $$ Answered by MJS_new last updated on 22/Dec/20 $$\int\frac{\sqrt{\mathrm{tan}\:{x}}}{\:\sqrt{\mathrm{tan}^{\mathrm{2}} \:{x}\:−\mathrm{1}}}{dx}=\int\sqrt{\frac{\mathrm{tan}\:{x}}{\mathrm{tan}^{\mathrm{2}} \:{x}\:−\mathrm{1}}}{dx}= \\ $$$$=−\frac{\mathrm{i}}{\:\sqrt{\mathrm{2}}}\int\sqrt{\mathrm{tan}\:\mathrm{2}{x}}{dx}…
Question Number 126529 by Study last updated on 21/Dec/20 Commented by Olaf last updated on 22/Dec/20 $$\mathrm{Why}\:{x}^{\frac{\mathrm{1}}{\mathrm{ln}{x}}} \:\mathrm{is}\:\mathrm{not}\:{e}^{\mathrm{ln}\left[{x}^{\frac{\mathrm{1}}{\mathrm{ln}{x}}} \right]} \:=\:{e}^{\frac{\mathrm{1}}{\mathrm{ln}{x}}\mathrm{ln}{x}} \:=\:{e}\:\mathrm{sir}\:? \\ $$$$\mathrm{Why}\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{not}\:{e}.{x}+\mathrm{C}\:? \\ $$…
Question Number 60976 by maxmathsup by imad last updated on 28/May/19 $${find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:{by}\:{use}\:{of}\:{integral}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left(\mathrm{2}{cos}\theta\right){d}\theta\:\:. \\ $$ Commented by maxmathsup by imad last…
Question Number 126510 by benjo_mathlover last updated on 21/Dec/20 $$\:\int\:\frac{{dx}}{\left({x}−\mathrm{2}\right)\sqrt{{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{8}}}\:? \\ $$ Answered by liberty last updated on 21/Dec/20 Answered by Ar Brandon last…
Question Number 126502 by benjo_mathlover last updated on 21/Dec/20 $$\:\:\int\:\frac{{dx}}{\:\sqrt{\mathrm{sin}\:^{\mathrm{5}} {x}\:\mathrm{cos}\:^{\mathrm{7}} {x}}}\:? \\ $$ Answered by MJS_new last updated on 21/Dec/20 $$\int\frac{{dx}}{\:\sqrt{\mathrm{sin}^{\mathrm{5}} \:{x}\:\mathrm{cos}^{\mathrm{7}} \:{x}}}= \\…
Question Number 60967 by maxmathsup by imad last updated on 27/May/19 $${study}\:{the}\:{integral}\:\int_{−\infty} ^{+\infty} \left(\mathrm{1}−{cos}\left(\frac{\mathrm{2}}{{x}^{\mathrm{2}} \:+\mathrm{1}}\right)\right){dx}\: \\ $$ Commented by abdo mathsup 649 cc last updated…
Question Number 60960 by maxmathsup by imad last updated on 27/May/19 $${find}\:\int_{−\infty} ^{+\infty} \:\:{tan}\left(\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\right){dx}\: \\ $$ Commented by mathsolverby Abdo last updated on 28/May/19…
Question Number 126493 by mathmax by abdo last updated on 21/Dec/20 $$\mathrm{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari last updated on…