Question Number 41302 by math khazana by abdo last updated on 05/Aug/18 $${calculate}\:\:\int_{\mathrm{1}} ^{+\infty} \:\:\frac{{dx}}{{x}^{\mathrm{2}} \sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}} \\ $$ Commented by maxmathsup by imad last…
Question Number 106830 by malwaan last updated on 08/Aug/20 $$\int\frac{\:{dx}}{\:\sqrt{{x}^{\mathrm{3}} \:}\:\:^{\mathrm{3}} \sqrt{\mathrm{1}\:+\:^{\mathrm{4}} \sqrt{{x}^{\mathrm{3}} }}}\:=\:? \\ $$ Commented by mathmax by abdo last updated on 07/Aug/20…
Question Number 41301 by math khazana by abdo last updated on 05/Aug/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:{e}^{−{ax}} {ln}\left(\mathrm{1}+{e}^{−{bx}} \right){dx}\:{with}\:{a}>\mathrm{0}\:{and} \\ $$$${b}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\frac{\partial{f}}{\partial{a}}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\frac{\partial{f}}{\partial{b}}\left({x}\right) \\ $$$$\left.\mathrm{3}\right){find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}}…
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Question Number 172352 by Mikenice last updated on 25/Jun/22 Answered by Mathspace last updated on 26/Jun/22 $$\int_{\mathrm{0}} ^{\infty} \:{x}^{\mathrm{6}} {e}^{−{x}} {cosx}\:{dx}={Re}\left(\int_{\mathrm{0}} ^{\infty} {x}^{\mathrm{6}} {e}^{−{x}+{ix}} {dx}\right)\:…
Question Number 41280 by math khazana by abdo last updated on 04/Aug/18 $${find}\:\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{arctan}\left({xt}^{\mathrm{2}} \right){dt} \\ $$ Commented by math khazana by abdo last…
Question Number 41279 by math khazana by abdo last updated on 04/Aug/18 $${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\:{arctan}\left({xt}^{\mathrm{2}} \right){dt}\:. \\ $$$${find}\:\:{a}\:{explicite}\:{form}\:{of}\:{f}^{'} \left({x}\right) \\ $$ Commented by maxmathsup by…
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Question Number 106809 by Study last updated on 07/Aug/20 $$\int{e}^{\mathrm{2}{x}} {sine}^{{x}} {dx}=?? \\ $$ Answered by bemath last updated on 07/Aug/20 $$\:\:\:\:\:@\mathrm{bemath}@ \\ $$$$\int\:\mathrm{e}^{\mathrm{x}\:} \mathrm{sin}\:\left(\mathrm{e}^{\mathrm{x}}…