Question Number 127468 by bramlexs22 last updated on 30/Dec/20 $$\:\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{x}^{\mathrm{3}} \:\mathrm{sin}\:\left(\lambda\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}} +\mathrm{4}}\:\mathrm{dx}\:=?\: \\ $$ Commented by bramlexs22 last updated on 30/Dec/20 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{both}\:\mathrm{sir} \\…
Question Number 127464 by bramlexs22 last updated on 30/Dec/20 Answered by liberty last updated on 30/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 61921 by maxmathsup by imad last updated on 11/Jun/19 $${let}\:{A}\:=\int_{−\infty} ^{+\infty} \:\:\:\:\:\frac{{x}+\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left(\:{x}^{\mathrm{2}} \:−\mathrm{2}{i}\right)}{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A} \\ $$$$\left.\mathrm{2}\right)\:{extract}\:{Re}\left({A}\right)\:{and}\:{Im}\left({A}\right)\:{and}\:{determine}\:{its}\:{values}\:\:\:\left({i}^{\mathrm{2}} =−\mathrm{1}\right) \\ $$ Commented by…
Question Number 127446 by mnjuly1970 last updated on 29/Dec/20 $$\:\:\:\:\:\:\:\:\:\:…{challanging}\:\:{integral}… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}\::: \\ $$$$\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\infty} \left({cos}\left({x}\right)−\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} \:}\right)\frac{{dx}}{{x}}\:=\:−\gamma\:\: \\ $$$$ \\ $$ Answered by mindispower last…
Question Number 127432 by mnjuly1970 last updated on 29/Dec/20 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\mathrm{CALCULUS}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\varnothing=\int_{−\infty} ^{\:+\infty} {cos}\left(\frac{\pi{x}^{\mathrm{2}} }{\mathrm{2}}\right){dx}=? \\ $$$$ \\ $$ Answered by Dwaipayan Shikari…
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Question Number 61885 by maxmathsup by imad last updated on 10/Jun/19 $${let}\:{I}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}+{i}\right)^{{n}} }\:\:{and}\:{J}\:=\int_{−\infty} ^{+\infty} \:\:\frac{{dx}}{\left({x}−{i}\right)^{{n}} } \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{I}\:{and}\:{J}\:{interms}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{thevalue}\:{of}\:{integral} \\ $$$${A}_{{n}} \:\:=\int_{−\infty}…
Question Number 127420 by liberty last updated on 29/Dec/20 $$\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{{x}−\mathrm{1}}{\:\sqrt{\mathrm{2}^{{x}} −\mathrm{1}}\:\mathrm{ln}\:\left(\mathrm{2}^{{x}} −\mathrm{1}\right)}\:{dx}\:? \\ $$ Answered by mnjuly1970 last updated on 29/Dec/20 $${solution}: \\…
Question Number 61884 by maxmathsup by imad last updated on 10/Jun/19 $${let}\:{f}_{{n}} \left({a}\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\frac{{cos}\left({nx}\right)}{\left({x}^{\mathrm{2}} +{x}\:\:+{a}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:\:\:{a}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{explicit}\:{form}\:{of}\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{convervenge}\:{of}\:\Sigma\:{f}_{{n}} \left({a}\right) \\ $$$$\left.\mathrm{3}\right)\:{determine}\:{also}\:{g}_{{n}}…
Question Number 61874 by aliesam last updated on 10/Jun/19 $$\int\frac{{xln}\left({x}\right)−{x}}{{ln}^{\mathrm{3}} \left({x}\right)}\:{dx} \\ $$ Commented by Prithwish sen last updated on 10/Jun/19 $$\int\left[\frac{\mathrm{x}}{\left[\mathrm{ln}\left(\mathrm{x}\right)\right]^{\mathrm{2}} }\:−\frac{\mathrm{x}}{\left[\mathrm{ln}\left(\mathrm{x}\right)\right]^{\mathrm{3}} }\:\right]\mathrm{dx} \\…