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Question Number 129696 by Eric002 last updated on 17/Jan/21
nice old question by sir m?th+et?s   ∫_0 ^∞ cos((x^3 /3)+tx)dx
$${nice}\:{old}\:{question}\:{by}\:{sir}\:{m}?{th}+{et}?{s}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} {cos}\left(\frac{{x}^{\mathrm{3}} }{\mathrm{3}}+{tx}\right){dx} \\ $$$$ \\ $$
Commented by mathdave last updated on 18/Jan/21
pls how did u hide d answer to d  question
$${pls}\:{how}\:{did}\:{u}\:{hide}\:{d}\:{answer}\:{to}\:{d} \\ $$$${question} \\ $$
Commented by mathdave last updated on 18/Jan/21
i want to view answer but i cant
$${i}\:{want}\:{to}\:{view}\:{answer}\:{but}\:{i}\:{cant} \\ $$
Commented by Eric002 last updated on 18/Jan/21
i didn′t hide any think sir
$${i}\:{didn}'{t}\:{hide}\:{any}\:{think}\:{sir} \\ $$
Commented by Eric002 last updated on 18/Jan/21
Commented by Eric002 last updated on 18/Jan/21
this is mr.mind is power solution if you  wanna viw the answer
$${this}\:{is}\:{mr}.{mind}\:{is}\:{power}\:{solution}\:{if}\:{you} \\ $$$${wanna}\:{viw}\:{the}\:{answer} \\ $$
Answered by mindispower last updated on 17/Jan/21
Ai(x)=(1/π)∫_0 ^∞ cos((t^3 /3)+xt)dt  known as Airy function  ⇒∫_0 ^∞ cos((x^3 /3)+tx)dx=πAi(t)
$${Ai}\left({x}\right)=\frac{\mathrm{1}}{\pi}\int_{\mathrm{0}} ^{\infty} {cos}\left(\frac{{t}^{\mathrm{3}} }{\mathrm{3}}+{xt}\right){dt} \\ $$$${known}\:{as}\:{Airy}\:{function} \\ $$$$\Rightarrow\int_{\mathrm{0}} ^{\infty} {cos}\left(\frac{{x}^{\mathrm{3}} }{\mathrm{3}}+{tx}\right){dx}=\pi{Ai}\left({t}\right) \\ $$

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