Question Number 33362 by prof Abdo imad last updated on 15/Apr/18 $${calculate}\:{by}\:{residus}\:{theorem} \\ $$$${I}\:=\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left(\pi{x}\right)}{\left(\mathrm{1}+{x}\:+{x}^{\mathrm{2}} \right)}{dx}\:. \\ $$ Commented by prof Abdo imad last…
Question Number 33356 by caravan msup abdo. last updated on 15/Apr/18 $${find}\:{the}\:{radius}\:{of}\:\sum_{{n}\geqslant\mathrm{0}} \frac{{n}^{\mathrm{2}} \:+{n}}{\mathrm{2}^{{n}} \:+{n}!}\:{x}^{{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33357 by caravan msup abdo. last updated on 15/Apr/18 $${find}\:{the}\:{rsdius}\:{of}\:{convergence}\:{for} \\ $$$${the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \left(\mathrm{1}\:+\frac{\mathrm{1}}{{n}}\right)^{{n}^{\mathrm{2}} } \:{x}^{{n}} \: \\ $$$$ \\ $$ Terms of…
Question Number 33353 by caravan msup abdo. last updated on 15/Apr/18 $$\left.{let}\:{x}\in\right]\mathrm{1},+\infty\left[\:{and}\lambda\:\in\left[−\mathrm{1},\mathrm{1}\right]\right. \\ $$$${give}\:{the}\:{integral}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{t}^{{x}−\mathrm{1}} \:{e}^{−{t}} }{\mathrm{1}−\lambda{e}^{−{t}} }\:{dt} \\ $$$${at}\:{form}\:{of}\:{serie}. \\ $$ Commented by…
Question Number 33351 by caravan msup abdo. last updated on 14/Apr/18 $${prove}\:{that} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{\left(−{lnx}\right)^{{p}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:={p}!\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{{p}+\mathrm{1}} } \\ $$$${p}\:{integr}. \\…
Question Number 33352 by caravan msup abdo. last updated on 15/Apr/18 $${let}\:{give}\:{S}\left({x}\right)=\sum_{{n}\geqslant\mathrm{0}} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{\:\sqrt{{x}+{n}}}\:,{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right){study}\:{the}\:{contnuity}\:,{derivsbility},{limits} \\ $$$${at}\:\mathrm{0}^{+} \:{and}\:+\infty \\ $$$$\left.\mathrm{2}\right)\:{we}\:{give}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{t}^{\mathrm{2}} } {dt}\:=\frac{\sqrt{\pi}}{\mathrm{2}}\:.{prove}\:{that}…
Question Number 98884 by mathmax by abdo last updated on 16/Jun/20 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{lnx}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{4}} }\mathrm{dx} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 33350 by caravan msup abdo. last updated on 14/Apr/18 $${prove}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:\frac{{cos}\left(\alpha{x}\right)}{{chx}}{dx}= \\ $$$$\mathrm{2}\:\sum_{{n}=\mathrm{0}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} \:\frac{\mathrm{2}{n}+\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} \:+\alpha^{\mathrm{2}} }\:. \\ $$ Commented by…
Question Number 98885 by M±th+et+s last updated on 16/Jun/20 $${find}\:{the}\:{range} \\ $$$$ \\ $$$${f}\left({x}\right)={log}_{\mathrm{4}} {log}_{\mathrm{2}} {log}_{\frac{\mathrm{1}}{\mathrm{2}}} \left({x}\right) \\ $$ Commented by MJS last updated on…
Question Number 33349 by caravan msup abdo. last updated on 14/Apr/18 $${prove}\:{that}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:{x}\left({x}−{ln}\left({e}^{{x}} −\mathrm{1}\right)\right){dx}=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{3}} } \\ $$ Commented by math…