Question Number 36438 by prof Abdo imad last updated on 02/Jun/18 $${let}\:{F}\left({x}\right)\:=\int_{{x}} ^{\frac{\mathrm{1}}{{x}}} \:\:\frac{{arctan}\left({t}\right)}{{t}}{dt} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:\frac{{dF}}{{dx}}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{F}\left({x}\right). \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated…
Question Number 36436 by prof Abdo imad last updated on 02/Jun/18 $${find}\:\:\int\:\:\:\:\:\frac{{sinx}}{\mathrm{1}+{cos}^{\mathrm{3}} {x}}{dx} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 02/Jun/18 $$=\int\frac{−{dt}}{\left(\mathrm{1}+{t}\right)\left(\mathrm{1}−{t}+{t}^{\mathrm{2}} \right)}\:\:\:\:{t}={cosx} \\…
Question Number 167510 by Mathspace last updated on 18/Mar/22 $${explicite}\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}\left({a}+{tan}^{\mathrm{2}} {x}\right){dx} \\ $$$${a}\geqslant\mathrm{2} \\ $$ Answered by ArielVyny last updated on 20/Mar/22 $${f}\left({a}\right)=\int_{\mathrm{0}}…
Question Number 101970 by Rohit@Thakur last updated on 05/Jul/20 $$\int_{\mathrm{0}} ^{\infty} \:\frac{{Cos}\left({ax}\right)}{{x}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:{dx} \\ $$ Answered by mathmax by abdo last updated on 06/Jul/20…
Question Number 36435 by prof Abdo imad last updated on 02/Jun/18 $${find}\:{the}\:{value}\:{of}\:{h}\left({t}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}+{tx}^{\mathrm{2}} \right)\:\:{with}\:\mid{t}\mid\leqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){dx} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} {ln}\left(\mathrm{1}−{x}^{\mathrm{2}} \right){dx}…
Question Number 36432 by prof Abdo imad last updated on 02/Jun/18 $${calculate}\:\:{I}\:=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:. \\ $$ Commented by abdo mathsup 649 cc last…
Question Number 36433 by prof Abdo imad last updated on 02/Jun/18 $${valculate}\:{f}\left({x}\right)=\:\int_{\mathrm{0}} ^{\mathrm{2}} \:\:\frac{\left({x}+\mathrm{2}\right)^{\mathrm{2}} }{\:\sqrt{{x}^{\mathrm{2}} \:+\mathrm{4}{x}+\mathrm{5}}}{dx} \\ $$ Commented by abdo.msup.com last updated on 02/Jun/18…
Question Number 36434 by prof Abdo imad last updated on 02/Jun/18 $${find}\:{g}\left({x}\right)\:=\int_{\mathrm{0}} ^{{x}} \:\:\:\frac{{e}^{−{t}} }{\:\sqrt{\mathrm{1}+{t}^{\mathrm{2}} }}{dt}. \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 02/Jun/18…
Question Number 36431 by prof Abdo imad last updated on 02/Jun/18 $${calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$ Commented by prof Abdo imad last updated…
Question Number 36429 by prof Abdo imad last updated on 02/Jun/18 $${let}\:\:\varphi\left(\lambda\right)\:=\:\int_{\frac{\lambda}{\pi}} ^{\frac{\pi}{\lambda}} \left(\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right){arctan}\left({x}\right){dx}\:{with}\:\lambda>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{simple}\:{form}\:{of}\:\varphi\left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\varphi^{'} \left(\lambda\right). \\ $$ Commented by abdo…