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 $$\:\:\:\:\:@\mathrm{bemath}@ \\ $$$$\int\:\mathrm{e}^{\mathrm{x}\:} \mathrm{sin}\:\left(\mathrm{e}^{\mathrm{x}}…
Question Number 41273 by prof Abdo imad last updated on 04/Aug/18 $${find}\:\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{+\infty} \:{arctan}\left({xt}^{\mathrm{2}} \right){dt}\:\:{with}\:{x}\:{fromR}\:. \\ $$ Commented by MJS last updated on 04/Aug/18 $$\mathrm{I}\:\mathrm{think}\:\mathrm{this}\:\mathrm{integral}\:\mathrm{is}\:\mathrm{divergent}…
Question Number 106808 by Study last updated on 07/Aug/20 $$\int{tan}\left({lnx}\right){dx}=??? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 106807 by Study last updated on 07/Aug/20 $$\int{sin}\left({ln}\mathrm{3}{x}\right){dx}=??? \\ $$ Answered by bemath last updated on 08/Aug/20 $$\:\:\:\:\:\:\:\:@\mathrm{bemath}@ \\ $$$$\mathrm{ln}\:\mathrm{3x}=\mathrm{u}\:\Rightarrow\mathrm{3x}=\mathrm{e}^{\mathrm{u}} \:;\:\mathrm{dx}\:=\:\frac{\mathrm{e}^{\mathrm{u}} \:\mathrm{du}}{\mathrm{3}} \\…
Question Number 41248 by Tawa1 last updated on 04/Aug/18 Commented by prof Abdo imad last updated on 04/Aug/18 $${changement}\:{x}=\sqrt{\mathrm{2}}{tant}\:\Rightarrow \\ $$$${I}\:=\:\int\:\:\frac{\sqrt{\mathrm{2}}\left(\mathrm{1}+{tan}^{\mathrm{2}} {t}\right){dt}}{\mathrm{8}\left(\mathrm{1}+{tan}^{\mathrm{2}} {t}\right)^{\mathrm{3}} }\:=\frac{\sqrt{\mathrm{2}}}{\mathrm{8}}\:\int\:\:\:\frac{{dt}}{\left(\mathrm{1}+{tan}^{\mathrm{2}} {t}\right)^{\mathrm{2}}…
Question Number 41246 by Raj Singh last updated on 04/Aug/18 Commented by prof Abdo imad last updated on 04/Aug/18 $${let}\:{A}\:=\:\int\:\:\:\:\frac{{sin}\left({lnx}\right)}{{x}^{\mathrm{3}} }{dx}\:{changement}\:{ln}\left({x}\right)={t} \\ $$$${give}\:{A}\:=\int\:\:\frac{{sin}\left({t}\right)}{{e}^{\mathrm{3}{t}} }\:{e}^{{t}} {dt}=\:\int\:\:{e}^{−\mathrm{2}{t}}…