Question Number 166940 by cortano1 last updated on 03/Mar/22 Answered by som(math1967) last updated on 03/Mar/22 $$\int\frac{{e}^{{x}} {x}+{e}^{{x}} }{{xe}^{{x}} \left(\mathrm{1}+{xe}^{{x}} \right)}{dx} \\ $$$${let}\:\:{xe}^{{x}} ={z}\Rightarrow\left({xe}^{{x}} +{e}^{{x}}…
Question Number 166939 by cortano1 last updated on 03/Mar/22 Answered by som(math1967) last updated on 03/Mar/22 $$\int\frac{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} −\mathrm{2}{x}^{\mathrm{2}} }{{x}^{\mathrm{6}} +\mathrm{1}}{dx} \\ $$$$\int\frac{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{\left({x}^{\mathrm{2}}…
Question Number 166916 by mnjuly1970 last updated on 02/Mar/22 $$ \\ $$$$\:\:\:\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:{H}_{\:{n}} }{{n}\left({n}+\mathrm{1}\right)}\:= \\ $$$$\:\:\:\:\:\:\:−−−−−− \\ $$$$\:\:\:\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}−\frac{\mathrm{1}}{{n}+\mathrm{1}}\:\int_{\mathrm{0}\:} ^{\:\mathrm{1}} {x}^{\:{n}−\mathrm{1}} {ln}\left(\mathrm{1}−{x}\:\right){dx} \\…
Question Number 101378 by Rohit@Thakur last updated on 02/Jul/20 $$\int_{\frac{\mathrm{1}}{{e}}} ^{{tanx}} \frac{{t}}{\mathrm{1}+{t}^{\mathrm{2}} }{dt}\:+\:\int_{\frac{\mathrm{1}}{{e}}} ^{{cotx}} \frac{\mathrm{1}}{{t}\left(\mathrm{1}+{t}^{\mathrm{2}} \right)}{dt} \\ $$ Commented by Dwaipayan Shikari last updated on…
Question Number 101373 by Dwaipayan Shikari last updated on 02/Jul/20 $$\underset{{n}\rightarrow\infty\:} {\mathrm{lim}}\underset{{r}=\mathrm{1}} {\overset{\mathrm{4}{n}} {\sum}}\frac{\sqrt{{n}}}{\:\sqrt{{r}}\left(\mathrm{3}\sqrt{{r}}+\mathrm{4}\sqrt{{n}}\right)^{\mathrm{2}} } \\ $$ Commented by Dwaipayan Shikari last updated on 02/Jul/20…
Question Number 35832 by abdo mathsup 649 cc last updated on 24/May/18 $${find}\:{the}\:{value}\:{of}\:\:{f}\left(\lambda\right)\:=\:\int_{−{a}} ^{{a}} \:\:\:\frac{{dx}}{\left(\lambda\:+_{} {x}^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} } \\ $$$$\lambda\in{R}\:. \\ $$ Commented by abdo.msup.com…
Question Number 35821 by prof Abdo imad last updated on 24/May/18 $${let}\:{f}\left({t}\right)\:=\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{e}^{−{ax}} \:−{e}^{−{bx}} }{{x}^{\mathrm{2}} }\:{e}^{−{tx}^{\mathrm{2}} } {dx}\:\:\:{with}\:{t}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{'} \left({t}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{a}\:{simple}\:{form}\:{of}\:{f}\left({t}\right) \\…
Question Number 166892 by mnjuly1970 last updated on 01/Mar/22 $$ \\ $$$$\:\:\:{solve}\:{in}\:\:\mathbb{R} \\ $$$$ \\ $$$$\:\:{i}:\:\:\:\:\lfloor\:{x}\:\lfloor\:{x}\rfloor\rfloor=\:\mathrm{3}{x} \\ $$$$ \\ $$$$\:\:{ii}\::\:\:\:\lfloor{x}\:\rfloor^{\:\mathrm{2}} −\mathrm{3}\:\lfloor{x}\:\rfloor\:+\mathrm{2}\:\leqslant\:\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:−−−−−− \\ $$$$…
Question Number 101345 by bobhans last updated on 02/Jul/20 $$\left(\mathrm{1}\right)\int\:\frac{\mathrm{sec}\:^{\mathrm{4}} {x}\:\mathrm{tan}\:{x}}{\mathrm{sec}\:^{\mathrm{4}} {x}+\mathrm{4}}\:{dx}= \\ $$$$\left(\mathrm{2}\right)\:\int{x}^{\mathrm{2}{x}} \left(\mathrm{2ln}{x}\:+\mathrm{2}\right)\:{dx}\:= \\ $$$$\left(\mathrm{3}\right)\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx}\:=\: \\ $$ Commented by john…
Question Number 101328 by M±th+et+s last updated on 01/Jul/20 $${this}\:{i}\:{a}\:{beautifull}\:{old}\:{question}\:{in}\:{the}\:{forum} \\ $$$${by}\:{sir}.{Ali}\:{Esam}\:{i}\:{Reposted}\:{it}\:{trying}\:{to} \\ $$$${find}\:{any}\:{idea}\:{to}\:{solve} \\ $$$$ \\ $$$${I}=\int_{−\mathrm{1}} ^{\mathrm{1}} \left(\frac{{sin}\left({x}\right)}{{sinh}^{−\mathrm{1}} \left({x}\right)}\right)\left(\frac{{sin}^{−\mathrm{1}} \left({x}\right)}{{sinh}\left({x}\right)}\right){dx} \\ $$$$ \\…