Question Number 40886 by prof Abdo imad last updated on 28/Jul/18 $${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\frac{{t}^{\mathrm{2}{p}+\mathrm{1}} {ln}\left({t}\right)}{{t}^{\mathrm{2}} −\mathrm{1}}{dt}\:=\frac{\pi^{\mathrm{2}} }{\mathrm{24}}\:−\frac{\mathrm{1}}{\mathrm{4}}\sum_{{k}=\mathrm{1}} ^{{p}} \:\frac{\mathrm{1}}{{k}^{\mathrm{2}} } \\ $$ Terms…
Question Number 40887 by prof Abdo imad last updated on 28/Jul/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{tln}\left({t}\right)}{{t}^{\mathrm{2}} −\mathrm{1}}{dt} \\ $$ Commented by prof Abdo imad last updated on…
Question Number 40884 by prof Abdo imad last updated on 28/Jul/18 $$\left.\mathrm{1}\right)\:{fond}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({t}\right)}{{t}^{\mathrm{2}} −\mathrm{1}}{dt} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left({t}\right)}{{t}^{\mathrm{4}} −\mathrm{1}}{dt} \\ $$ Answered by maxmathsup…
Question Number 40883 by prof Abdo imad last updated on 28/Jul/18 $${find}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{t}^{{p}} }{{e}^{{t}} −\mathrm{1}}{dt}\:{with}\:{p}\in{N}^{\bigstar} \\ $$ Answered by maxmathsup by imad last updated…
Question Number 40870 by math khazana by abdo last updated on 28/Jul/18 $${fnd}\:\:\int\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctan}\left({x}−\frac{\mathrm{1}}{{x}}\right){dx}\:. \\ $$ Commented by maxmathsup by imad last updated on 29/Jul/18…
Question Number 40868 by math khazana by abdo last updated on 28/Jul/18 $${calculate}\:\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{x}}{{sinx}}{dx}\:\:. \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 29/Jul/18 Commented…
Question Number 106392 by Ar Brandon last updated on 05/Aug/20 $$\int_{\mathrm{0}} ^{\infty} \sqrt{\frac{\mathrm{2t}+\mathrm{3}}{\mathrm{5t}^{\mathrm{3}} +\mathrm{3t}^{\mathrm{2}} +\mathrm{2}}}\mathrm{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 106391 by Ar Brandon last updated on 05/Aug/20 $$\int\mathrm{e}^{\mathrm{2x}^{\mathrm{2}} +\mathrm{x}} \mathrm{dx} \\ $$ Answered by Sarah85 last updated on 05/Aug/20 $${t}=\sqrt{\mathrm{2}}\left({x}+\frac{\mathrm{1}}{\mathrm{4}}\right)\:\Leftrightarrow\:{x}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{t}−\frac{\mathrm{1}}{\mathrm{4}}\:\Rightarrow\:{dx}=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}{dt} \\ $$$$\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\int\mathrm{e}^{{t}^{\mathrm{2}}…
Question Number 171910 by Tawa11 last updated on 21/Jun/22 $$\int\:\frac{\mathrm{dx}}{\mathrm{9}\:\:\:−\:\:\:\mathrm{4x}^{\mathrm{2}} } \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{trigonometric}\:\mathrm{substitution}. \\ $$ Answered by aleks041103 last updated on 21/Jun/22 $$\int\frac{{dx}}{\mathrm{9}−\mathrm{4}{x}^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{9}}\int\frac{{dx}}{\mathrm{1}−\left(\frac{\mathrm{2}{x}}{\mathrm{3}}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{9}}\:\frac{\mathrm{3}}{\mathrm{2}}\int\frac{{du}}{\mathrm{1}−{u}^{\mathrm{2}}…
Question Number 40830 by math khazana by abdo last updated on 28/Jul/18 $${find}\:\int\:\sqrt{\mathrm{2}+{tan}^{\mathrm{2}} {t}}{dt} \\ $$ Commented by maxmathsup by imad last updated on 31/Jul/18…