Question Number 34110 by tanmay.chaudhury50@gmail.com last updated on 30/Apr/18 Commented by tanmay.chaudhury50@gmail.com last updated on 30/Apr/18 $${i}\:{am}\:{sharing}\:{dome}\:{important}\:{formula}\: \\ $$ Commented by NECx last updated on…
Question Number 34107 by tanmay.chaudhury50@gmail.com last updated on 30/Apr/18 Commented by tanmay.chaudhury50@gmail.com last updated on 30/Apr/18 $${i}\:{am}\:{new}\:{in}\:{this}\:{forum}\:{i}\:{am}\:{sharing}\:{some}\:{impotsnt}\:{formula} \\ $$ Commented by math khazana by abdo…
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Question Number 165164 by mnjuly1970 last updated on 26/Jan/22 Answered by aleks041103 last updated on 27/Jan/22 $${f}\left({x}\right)=\mid\left({x}+{a}\right)\left({x}^{\mathrm{2}} +\left({a}+\mathrm{2}\right){x}+\mathrm{1}\right)\mid \\ $$$${for}\:{this}\:{to}\:{be}\:{non}−{diff}\:{at}\:{only}\:{one}\:{point} \\ $$$${we}\:{need}\:\left({x}+{a}\right)\left({x}^{\mathrm{2}} +\left({a}+\mathrm{2}\right){x}+\mathrm{1}\right)\:{to} \\ $$$${change}\:{signs}\:{only}\:{once}.\:{Since}\:{one}\:{always}…
Question Number 99576 by mathmax by abdo last updated on 21/Jun/20 $$\left.\mathrm{1}\right)\mathrm{let}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\:\mathrm{t}^{\mathrm{a}−\mathrm{1}} \mathrm{ln}\left(\mathrm{t}\right)}{\mathrm{1}+\mathrm{t}}\:\mathrm{dt}\:\:\:\mathrm{with}\:\mathrm{0}<\mathrm{a}<\mathrm{1}\:\:\:\mathrm{prove}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{a}\right)\mathrm{is}\:\mathrm{convergent}\:\mathrm{and}\:\mathrm{determine} \\ $$$$\mathrm{it}\:\mathrm{value} \\ $$$$\left.\mathrm{2}\right)\mathrm{calculate}\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{lnt}}{\left(\mathrm{1}+\mathrm{t}\right)\sqrt{\mathrm{t}}}\mathrm{dt} \\ $$$$\left.\mathrm{3}\right)\mathrm{calculate}\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{lnt}}{\left(^{\mathrm{3}}…
Question Number 99578 by mathmax by abdo last updated on 21/Jun/20 $$\left.\mathrm{1}\right)\mathrm{calculate}\:\:\mathrm{U}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\mathrm{e}^{−\mathrm{nx}^{\mathrm{4}} } \mathrm{dx}\:\:\mathrm{and}\:\mathrm{determine}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{n}^{\mathrm{4}} \:\mathrm{U}_{\mathrm{n}} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\mathrm{nature}\:\mathrm{of}\:\mathrm{the}\:\mathrm{serie}\:\Sigma\:\mathrm{U}_{\mathrm{n}} \\ $$ Answered by…
Question Number 165097 by abdullahhhhh last updated on 26/Jan/22 Answered by Eulerian last updated on 26/Jan/22 $$\: \\ $$$$\:\mathrm{By}\:\mathrm{using}\:\mathrm{King}\:\mathrm{rule}\:\mathrm{of}\:\mathrm{integration}: \\ $$$$\:\int_{\frac{\pi}{\mathrm{6}}\:} ^{\:\frac{\pi}{\mathrm{3}}} \:\left(\mathrm{cot}\:\mathrm{x}\right)^{\left(\mathrm{tan}\:\mathrm{x}\right)^{\left(\mathrm{cot}\:\mathrm{x}\right)} } \:−\:\left(\mathrm{tan}\:\mathrm{x}\right)^{\left(\mathrm{cot}\:\mathrm{x}\right)^{\left(\mathrm{tan}\:\mathrm{x}\right)}…
Question Number 34021 by prof Abdo imad last updated on 29/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{+\infty} \:\:\:\frac{{cos}\left(\alpha{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left(\:{x}^{\mathrm{2}} +\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{3}\right)}{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:+\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{3}\right)} \\…
Question Number 99557 by adeyemi last updated on 21/Jun/20 $$ \\ $$$$\Lambda=\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{Li}_{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{1}+\mathrm{x}}\right)+\mathrm{Li}_{\mathrm{3}} \left(\frac{\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)+\mathrm{Li}_{\mathrm{4}} \left(\frac{\mathrm{x}+\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}}\right)\right)\mathrm{dx} \\ $$$$\mathrm{Li}_{\mathrm{n}} \left(\mathrm{z}\right)=\mathrm{polylogarithm}\:\mathrm{function}. \\ $$$$\mathrm{by}\:\mathrm{adeyemi}. \\ $$$$…
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