A RIDICULOUSLY AWESOME INTEGRAL!!!! int 0 to infty (sin(x^2+1/x^2))^3

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The fresnel integrals solved using Feynman's trick:

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The man is back with some more exciting maths. Let us all cheer!

slavinojunepri
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Could use the trig identity that has sin(x)+cos(x) = sqrt(2)*sin(x+pi/2) at the end to simply the result a little bit. It would be only in terms of sines at least.

SuperSilver
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Really it is interesting integral. Thank you for your smart solution.

MrWael
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He's back! Finally! the last remaining days of my summer vacation have been bejeweled by the funny math man. I though of solving it by immediatly using the weistrauss sub, and then applying the trig identity to finish it off with IBP.

manstuckinabox
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Начиная с этого момента 4:25 перед членом sin(3u^2+6) стоит знак "-" дальше вы вводите обозначение I2, потом после решения. А с момента 9:17 знак потерян "+" вместо "-". Соответственно в решении 9:50 также пропущен знак "-".

YahontAction
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Welcome back man, great video as always

gabriel_talih
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You have missed a minus before I 2 . Thank you for the exercise

roykamaan
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Bro which program do you use to write the solution?

hakikatcfischer
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Amazing!
could you please suggest me textbooks for advanced calculus that demonstrate these techniques to solve these improper integrals?

ahmedamir
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Glad you're back!
One question, if the integral was - inf to +inf, what would the bounds of integration be? How would someone go about that? (I know in this case it's an even integrand but what if it wasn't?)

amidhmi
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Hi math 505 from where do you get these integrals? Do you make them yourselves and verify with wolfram alpha?

anupamamehra
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Nice, how the sqrt(pi/8) and √3 came out

Chris_
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Too much difficult. I lose heart when trying to solve integrals like this one.

Mario_Altare
welcome to shbcf.ru