I would start with integration by parts then use linearity to calculate integrals separately Only one integral need to be calculated with power series expansion other can be calculated by easy to guess substitutions
Your videos are awesome. Keep up the great work. +1 sub. I only wanted mention that it would be nicer to have some more diverse content. I've watched your number theory pblem (very cool).. it would be nice to have some more. Inequalities also are interesting, differential equations etc... thank you once again.
Thanks. I scribbled this last night and it was during the solution development that I realized that the most efficient way to evaluate Eular's log trig integrals is using that series expansion of ln(cos(x)).
I would like you to pause at 2:30- where you have taken the result from your earlier video - whichis actually (- pi/2*ln2) and also DOES NOT match with the same integral evaluated by BlackpenRedpen using Feynman technique (it is +pi/2*ln2). Can you please clarify this? Your method otherwise is perfect. Appreciate it
Hi, great video. I'm kind of a beginner at this, but would it be possible to do partial fraction decomposition? Get a Taylor series for arctan(x) and equate coefficients?
Please stop at 2:47 - the integral of [cos(t)/(sin(t)+cos(t)] | 0 to pi/2 can be computed very easily- just apply the rule : [int f(x)dx | 0 -a] = intf(a-x)dx| |0-a. where "a" here is =pi/2. This gives a very simple answer = pi/4. Can you please review this?
@@maths_505 i think they meant 3:34 and yes the integral is a prime candidate for using King's property, which gives the answer as a/2, which in this case is pi/4. however the part they misunderstood is that its one part in ibp and not thr entire integral by itself so its of no use here
I was wondering where the series expansion 's gunna arive. Question: Can we use fourier series to construct some functional equation from the series expansion at 16:48?
@@leif1075 Isn't multiplying by 1/sqrt2 a high-school level trick? It's one of the few basic cases of "multiply by 1". On the other hand that "sine x equals 1 minus cosine^2×" should have ^2 over sinx OR square root over the other part. It would have been an absolute mess to work with.
@@leif1075 If something is in high school curriculum then it's something a person should deduce on their own later on. And if that's not something that is teached where you live then blame your education system. "sinx + cosx" absolutely begs to be turned into one trig function, the same way square roots might "beg" to be removed from the denominator by multiplying by 1. Of course that doesn't mean it's going to be useful, but it's one of the tools/tricks you can consider using in this or that situation (which is like 90% of solving integrals on your own anyway).
Hey. Maybe I'm alone at this, but I find that the more challenging the integrals - given my abilities - the more I care about your mind process for deciding a certain strategy... and the less I care about the actual solution process. Out of the dozens of techniques you use, it just feels random to have a series of 4-5 techniques used to get the result... why those? why at that point? Did you try something promising that didn't work? Would you also try something else? I would find the videos much more interesting if you included it. Thanks for the great content anyways!
Behind every integral, DE and series on my channel there are write ups that went wrong. Then there are write ups that went right and then I said hold up I can come up with something better. Thank you so much for acknowledging how tough it is to create this content and sometimes are so bad I've actually mentioned them in the video😂
So just learn and apply as much as you can and the thought process will become muscle memory for you. Don't worry about it.....I'm not the smartest but f**k I know I'm persistent
You can find alot of em on stackexchange and the internet and some of em (like this one here) I just make em up by piecing together functions like "wonder what'll happen if I just throw in an inverse tangent" 😂😂😂
I'm fukced up. Wasted 4 hours but there isn't any other way to do it! Who finds this math ? You or other youtuber? Big fan friend. Or should I said sir?
Adesso lo faccio,.... Però aspetta 2/3 giorni!!!... Uso Feymann con arctg(ax), nella derivata se ne va una x.. poi userò gli integrali razionali (5 equazioni in 5 incognite...)
@@faisaliqbal4669 wo bhi practice or study se hi solve hoga yar. Try solving as many problems as possible and look at alternative solutions. It'll help you think.
@@maths_505 I like Andrew Tate a lot he teaches these young boys to not be a slave to women and become Men. And don’t care what women think about you. I have been saying the same things since 2001.
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This one was pretty tough for me ahah. I was able to understand your solution/explanation though, thank you for sharing!
Amazing solution for this monster integral. Thank you.
I would start with integration by parts then
use linearity to calculate integrals separately
Only one integral need to be calculated with power series expansion
other can be calculated by easy to guess substitutions
Your videos are awesome. Keep up the great work. +1 sub.
I only wanted mention that it would be nicer to have some more diverse content. I've watched your number theory pblem (very cool).. it would be nice to have some more. Inequalities also are interesting, differential equations etc... thank you once again.
Great man. Thank you. What's the name of the blackboard software you are using here?
Amazing solution development!
Thanks. I scribbled this last night and it was during the solution development that I realized that the most efficient way to evaluate Eular's log trig integrals is using that series expansion of ln(cos(x)).
Oh and I'm finally gonna use the Lambert W function in my next video😂
@@maths_505make sure it also contains the gamma function!
@@robertsandy3794 haha kinda mandatory for integrals on this channel
I would like you to pause at 2:30- where you have taken the result from your earlier video - whichis actually (- pi/2*ln2) and also DOES NOT match with the same integral evaluated by BlackpenRedpen using Feynman technique (it is +pi/2*ln2).
Can you please clarify this? Your method otherwise is perfect. Appreciate it
The answer is indeed pi/2*ln2
Hi, great video. I'm kind of a beginner at this, but would it be possible to do partial fraction decomposition? Get a Taylor series for arctan(x) and equate coefficients?
Well we can use a Taylor series for arctan x
But what do you mean by equating coefficients?
@@maths_505 I mean like how you typically solve an integral of a rational function, setting the constant terms equal, then the linear terms, etc
Ohhh....yeah we could but that would be a much longer route than actually getting rid of the arctan term
Please stop at 2:47 - the integral of [cos(t)/(sin(t)+cos(t)] | 0 to pi/2 can be computed very easily- just apply the rule : [int f(x)dx | 0 -a] = intf(a-x)dx| |0-a.
where "a" here is =pi/2. This gives a very simple answer = pi/4. Can you please review this?
Review the video and your comment. The 2nd integral doesn't simplify to what you're saying because the numerator is tcos(t) not just cos(t).
@@maths_505 i think they meant 3:34 and yes the integral is a prime candidate for using King's property, which gives the answer as a/2, which in this case is pi/4. however the part they misunderstood is that its one part in ibp and not thr entire integral by itself so its of no use here
@@ingenuity23-yg4ev 'They' :-)
can you workout the partial fraction for me? It went 2 fast for me, I've never seen PF used on formulas outside quadratics
Oh that's easy to visualise.
Replace tan(t) by some other variable, say x, and then you need the PFD for 1/(x)(x+1)
I was wondering where the series expansion 's gunna arive.
Question: Can we use fourier series to construct some functional equation from the series expansion at 16:48?
😂😂😂
Gotta love an infinite series ❤
Especially that sexy log cosine series 🔥🔥🔥🔥
Well fourier is the og way to go in deriving that series expansion.
@@maths_505 it really shows LOL, screamed eigenfunction
@@leif1075 Isn't multiplying by 1/sqrt2 a high-school level trick? It's one of the few basic cases of "multiply by 1".
On the other hand that "sine x equals 1 minus cosine^2×" should have ^2 over sinx OR square root over the other part. It would have been an absolute mess to work with.
@@leif1075 If something is in high school curriculum then it's something a person should deduce on their own later on. And if that's not something that is teached where you live then blame your education system.
"sinx + cosx" absolutely begs to be turned into one trig function, the same way square roots might "beg" to be removed from the denominator by multiplying by 1. Of course that doesn't mean it's going to be useful, but it's one of the tools/tricks you can consider using in this or that situation (which is like 90% of solving integrals on your own anyway).
What's integral of 1/√(sin x) wrt x , with limits 0 to π/2
Use the geometric form of the beta function. It'll give you the answer in a couple of lines.
Probably Feynman's trick would have been easier.
Hey. Maybe I'm alone at this, but I find that the more challenging the integrals - given my abilities - the more I care about your mind process for deciding a certain strategy... and the less I care about the actual solution process.
Out of the dozens of techniques you use, it just feels random to have a series of 4-5 techniques used to get the result... why those? why at that point? Did you try something promising that didn't work? Would you also try something else? I would find the videos much more interesting if you included it.
Thanks for the great content anyways!
Behind every integral, DE and series on my channel there are write ups that went wrong. Then there are write ups that went right and then I said hold up I can come up with something better. Thank you so much for acknowledging how tough it is to create this content and sometimes are so bad I've actually mentioned them in the video😂
So just learn and apply as much as you can and the thought process will become muscle memory for you. Don't worry about it.....I'm not the smartest but f**k I know I'm persistent
What is source of wonderful looking integrals?
You can find alot of em on stackexchange and the internet and some of em (like this one here) I just make em up by piecing together functions like "wonder what'll happen if I just throw in an inverse tangent" 😂😂😂
I'm fukced up. Wasted 4 hours but there isn't any other way to do it!
Who finds this math ? You or other youtuber?
Big fan friend. Or should I said sir?
Friend is good. This integrals custom made like alot of the integrals you'll find here.
Adesso lo faccio,.... Però aspetta 2/3 giorni!!!... Uso Feymann con arctg(ax), nella derivata se ne va una x.. poi userò gli integrali razionali (5 equazioni in 5 incognite...)
Woah......that's ambitious yo😂
@@maths_505..potrei usare Per Parti,visto che ho 1/1+x^2,ma poi ho un integrale con dentro una arctg1,boh..
That's the fun integral🔥🔥🔥
@@maths_505 ho trovato I'(a) ma la primitiva I(a) é impossibile da calcolare.. I=I(1)
taylor of Ln(2cos(x)) is not true
Sorry, I didn't see the equality cos(x) on the right side
Bro how to get excellent manipulation in maths
Practice
Practice
And
Practice
Bhai practice me hi problem hota h ki how think
@@faisaliqbal4669 wo bhi practice or study se hi solve hoga yar. Try solving as many problems as possible and look at alternative solutions. It'll help you think.
@@maths_505how you spoke hindi language 😮
@@Maths_3.1415 I'm Pakistani so I can speak urdu.
I am theaving your problems for my videos. I guess that's fine. But I don't have a very good accent.
I think Andrew Tate would love this video.
When I teach physics, I call the universal gravitational constant top G too😂
It's always gets a laugh outta the boys.
@@maths_505 lol that’s cool bro
Hey look it seems fitting .....that gravitational constant is f**king universal so its gotta be top G😎😂
@@maths_505 exactly bro lol
@@maths_505 I like Andrew Tate a lot he teaches these young boys to not be a slave to women and become Men. And don’t care what women think about you. I have been saying the same things since 2001.