show-that-1-x-2-1-dx-is-unsolvable-

Question Number 153063 by talminator2856791 last updated on 04/Sep/21

$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{show}\:\mathrm{that} \\ $$$$\: \\ $$$$\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:\:{dx} \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{is}\:\mathrm{unsolvable} \\ $$$$\: \\ $$

Commented by amin96 last updated on 04/Sep/21

$$ \\ $$very interesting question

Commented by MJS_new last updated on 04/Sep/21

$$\mathrm{can}\:\mathrm{we}\:\mathrm{solve}\:\int{x}^{{x}} {dx}\:\mathrm{or}\:\int\frac{{dx}}{{x}^{{x}} }\:? \\ $$

Commented by talminator2856791 last updated on 04/Sep/21

$$\:\mathrm{no}. \\ $$$$\:\mathrm{those}\:\mathrm{cant}\:\mathrm{be}\:\mathrm{solved}. \\ $$$$\:\mathrm{but}\:\mathrm{how}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{that}? \\ $$

Commented by MJS_new last updated on 04/Sep/21

$$\mathrm{I}\:\mathrm{don}'\mathrm{t}\:\mathrm{think}\:\mathrm{we}\:\mathrm{can}\:\mathrm{prove}\:\mathrm{it}. \\ $$

Commented by mathdanisur last updated on 04/Sep/21

$$=\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\:\frac{\left(-\mathrm{1}\right)^{\mathrm{n}} }{\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} }\:\right] \\ $$

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