From I have seen in complex analysis, ln is often used to denote the multivalued logarithm function, whereas Log represents the principal branch of the natural logarithm.
Using some substitutions, you can show that evaluating this integral is equivalent to showing that the integral from 0 to infinity of (cos(2x)*log(x) + pi/2*sin(x))/(x^2 + 1)*dx = 0, which I think might be an even more interesting result. This makes me think there might be a solution to this integral using symmetry, but I have no idea how to go about showing that.
Oh hey you can evaluate this integral using comple- oh ok.. man that;s such a beutiful integral, you're supply is always up to the damand, best math dealer out here. 5:00 I think it goes like this ln : Real Logarithm log : any branch of the logarithm Log: principle branch of the logarithm
Very cool to see sin x appear by combining the two halves of the integral. Do we need to consider the little gamma integral at all? There's no discontinuty at z=0.
This is second-year university level calculus, so I fully expect log = natural logarithm. Ln is for high school or introductory calculus and should be matured out of as quickly as possible.
Indeed.... But ofcourse I wasn't referring to you my fellow knight of dark math😂 I was referring to those who are just entering the dark realm of higher math.... However I do find it strange that many great books in higher math still use ln....I think that could either stem from rebellion towards complex analysis or maybe they just don't want to get rid of the old notation.
Absolutely LOVE your content. And, i have to say, with something this fiddly", when you go "What the Fuck" ... it just makes me smile. I say this all the time when solving problems!! COOL, man! Is there anywhere where you do / could tell us a bit about yourself / your background? I really rate you, and think your stuff is GREAT. Really enjoy it, actually. CHEERS! Patrick.
Hi, can someone please explain why 1/|R²e²ᶲⁱ + 4| ≤ 1/(R² - 4)? Edit: Ok I think I figured it out actually. I'm just confused why he said it like it is trivial.
From I have seen in complex analysis, ln is often used to denote the multivalued logarithm function, whereas Log represents the principal branch of the natural logarithm.
your skills are insane mate. great videos, nice and challenging
22:27
Int (cosx)/(x²+4) at interval (-inf,inf)=pi/2e²
Love it! Keep making amazing videos!
Using some substitutions, you can show that evaluating this integral is equivalent to showing that the integral from 0 to infinity of (cos(2x)*log(x) + pi/2*sin(x))/(x^2 + 1)*dx = 0, which I think might be an even more interesting result. This makes me think there might be a solution to this integral using symmetry, but I have no idea how to go about showing that.
WolframAlpha does not like that definite integral.
Would you please do this integral using the Feynman Technique please.
This is it! Thanks!
Called it!
Oh hey you can evaluate this integral using comple- oh ok..
man that;s such a beutiful integral, you're supply is always up to the damand, best math dealer out here.
5:00 I think it goes like this
ln : Real Logarithm
log : any branch of the logarithm
Log: principle branch of the logarithm
We always need the principle branch so log all the way🥳
Sympathy for your cat! Give it a bowl of fresh milk!
Fascinating !
Very cool to see sin x appear by combining the two halves of the integral.
Do we need to consider the little gamma integral at all? There's no discontinuty at z=0.
What's log(z) at z=0?
Thanks, I'm not sure how I missed that; the video even explicitly points it out.
This is second-year university level calculus, so I fully expect log = natural logarithm. Ln is for high school or introductory calculus and should be matured out of as quickly as possible.
Indeed....
But ofcourse I wasn't referring to you my fellow knight of dark math😂
I was referring to those who are just entering the dark realm of higher math....
However I do find it strange that many great books in higher math still use ln....I think that could either stem from rebellion towards complex analysis or maybe they just don't want to get rid of the old notation.
Can't hurt to be cautious 🙂
Absolutely LOVE your content. And, i have to say, with something this fiddly", when you go "What the Fuck" ... it just makes me smile. I say this all the time when solving problems!! COOL, man! Is there anywhere where you do / could tell us a bit about yourself / your background? I really rate you, and think your stuff is GREAT. Really enjoy it, actually. CHEERS! Patrick.
I'll do a video on that someday
It’s really cool..Waiting to see more like this❤️❤️
Pure Awesomeness dude...... #complexanalysis
Do integral from 0 to pi/4 of arctan(sqrt((1-tan(x))/2))
Is there another way to solve the integral? For example, Laplace or Fayman
You can split it into 2 integrals and perhaps find out new ways to evaluate it
Hi, can someone please explain why 1/|R²e²ᶲⁱ + 4| ≤ 1/(R² - 4)?
Edit: Ok I think I figured it out actually. I'm just confused why he said it like it is trivial.
Now we talking ....
Greetings to your cat.
The cat reciprocates
I can solve it by one trick
lnx=int [2yx^2/(1+x^2y^2)
-2y/(1+y^2)] dy from 0 to infinity