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Question Number 110145 by mathdave last updated on 27/Aug/20
prove that  ∫_1 ^∞ ((ln(x))/(1+x+x^2 +x^3 ))dx=(G/2)−(π^2 /(32))  G(catalan constant)
$${prove}\:{that} \\ $$$$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{ln}\left({x}\right)}{\mathrm{1}+{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} }{dx}=\frac{{G}}{\mathrm{2}}−\frac{\pi^{\mathrm{2}} }{\mathrm{32}} \\ $$$${G}\left({catalan}\:{constant}\right) \\ $$
Answered by mnjuly1970 last updated on 27/Aug/20
 edited ....   m.n.july 1970 ...⇓⇓⇓
$$\:{edited}\:…. \\ $$$$\:{m}.{n}.{july}\:\mathrm{1970}\:…\Downarrow\Downarrow\Downarrow \\ $$
Answered by mnjuly1970 last updated on 27/Aug/20
Commented by mathdave last updated on 27/Aug/20
brillant workdone keep it up
$${brillant}\:{workdone}\:{keep}\:{it}\:{up} \\ $$$$ \\ $$$$ \\ $$
Commented by mnjuly1970 last updated on 27/Aug/20
thank you for your nice  problems...peace be upon  you...
$${thank}\:{you}\:{for}\:{your}\:{nice} \\ $$$${problems}…{peace}\:{be}\:{upon} \\ $$$${you}… \\ $$

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