I have a suggestion: Can u evaluate ur integrals in the future on a laptop screen using a pen tablet with commentary on how the steps you're taking work? This will make the session more engaging and interactive than simply having to watch a silent vid and things done on pen-and-paper. It's ur choice whether u want webcam or not - both work and fit the atmosphere in their own way. However, I strongly suggest the digital way for ur videos to be - with the screen and the pen tablet with commentary. No more of pen-and-paper.
@@Gust52 personally I find it more engaging with the viewer the original way because, it makes you think why he does a step, and after some time you get really good at looking ahead and seeing patterns in the integrals in his videos. Thanks to his videos I learned so fast I went from not know what "integral" means to Putnam questions in like 2-3 months (thank you♥️) Although I can kinda understand you, early on I couldn't really understand why he did a step, there are a couple of solutions to this but non are even coming close to touching the content on this channel: 1. First of all this channel (in my humble opinion) is to people who already had some experience with integrals, instead there are TH-camrs who explain every step in the process and teach methods, I recommend pairing this channel with some others and not committing the mistake of starting of with this stuff like I did. 2.I personally think this channel is plenty enough, if he wants *Integrals for you* can make another channel using your suggestion BUT NOT change the content on this channel, but no pressure this channel is amazing as it is! Once again thanks for everything!🫡
@@gabyshavit8539 Ty for taking the time to write such an insightful response man. I appreciate it 👍 *But I think u may have misunderstood me regarding commentary* : I'm suggesting commentary cuz otherwise the vids seem boring with such silence persisting throughout everywhere. Commentary is needed so viewers feel that there is indeed someone there who's doing the things and making an engaging atmosphere. It arouses interest. If one is just dead silent, the vid will seem plain and boring & like some AI just printing out the answer to u without any interest. Commentary for the steps was only a part of it. Commentary is needed as an intro, for engagement, and outro for ANY vid. It gives rise to engagement & attention, which are vital to make viewers stay, watch and take time to comment. Otherwise they wouldn't feel they're watching a youtuber but some supplement college vid. They wouldn't feel a part of the production of a content creator, but only a viewer of some random vid. *Hence commentary is vital to increase views and comments.* Many math youtubers like bprp & peyam have more viewership cuz of commentating and making a fun atmosphere while teaching. So, this channel too should do the same.
@@Gust52Thank you for the response! I got your point now, the thing is adding commentary to this channel will just kinda mess with what is on it because part of the learning process of integrals at least in my opinion is doing it yourself, adding commentary may be nice but it shouldn't be to this exact channel, instead maybe a new channel for this will work but this style of content on this channel at least for me feels more engaging, if you find yourself watching the videos in boredom you can try to make it more interesting by actually trying to solve the integral yourself especially if it is a hard one, just not changing the style on this channel it really helped me learn fast and achieve mastery of integrals really fast and I know there are some other people who did too. Anyway I understand you the content doesn't work for anyone, but in my opinion this is the best way to learn integrals really quick for anyone but only after having a nice base of them or else you're gonna have a hard time.
Hi I searched on your website for the integral of arctanx/x a while ago and after watching this video I got reminded of it, have you ever done this integral? because I couldn't solve it in the end just thought it's a nice challenge
Hi! The integral of arctan(x)/x is a non-elementary integral, it cannot be expressed in terms of finite standard functions... However the integral of arctan(x)/x^2 can be integrated 😉
@@IntegralsForYou thanks it nice to know it's not a skill issue, well I can also assume the integral of ln(x+1)/(1+x^2) aka the integral of ln(tanx+1) (without bounds) has the same issue right?
@@gabyshavit8539 Yes, the integrals of ln(x+1)/(1+x^2) or ln(tan(x)+1) are also non-elementary... 🥲 If we had bounds maybe we could integrate it but I don't know how to
@@gabyshavit8539 Because in general we need the derivative multiplying the functions you asked, or maybe something similar. For the case of ln(x+1)/(1+x^2) we see that there is no derivative multiplying anything so the only possible way is doing it by parts. When I do parts I see that it is impossible to continue... maybe also by my experience. After these checks, I can be wrong but I am 95% sure it is a non-elementary integral.
𝐏𝐥𝐞𝐚𝐬𝐞 𝐒𝐔𝐁𝐒𝐂𝐑𝐈𝐁𝐄 𝐭𝐨 𝐦𝐲 𝐧𝐞𝐰 𝐜𝐡𝐚𝐧𝐧𝐞𝐥 𝐃𝐞𝐫𝐢𝐯𝐚𝐭𝐢𝐯𝐞𝐬 𝐅𝐨𝐫𝐘𝐨𝐮! www.youtube.com/@DerivativesForYou 𝐓𝐡𝐚𝐧𝐤 𝐲𝐨𝐮! ❤
Thanks. You make me improve my integration skills!
Glad to hear that! ❤
Many thanks
My pleasure! ❤
Very nice!
Thank you! ❤
I have a suggestion:
Can u evaluate ur integrals in the future on a laptop screen using a pen tablet with commentary on how the steps you're taking work?
This will make the session more engaging and interactive than simply having to watch a silent vid and things done on pen-and-paper.
It's ur choice whether u want webcam or not - both work and fit the atmosphere in their own way.
However, I strongly suggest the digital way for ur videos to be - with the screen and the pen tablet with commentary.
No more of pen-and-paper.
Hi! Thank you very much for your suggestion! I'll think about it, maybe it is time to change a little bit...
@@Gust52 personally I find it more engaging with the viewer the original way because, it makes you think why he does a step, and after some time you get really good at looking ahead and seeing patterns in the integrals in his videos.
Thanks to his videos I learned so fast I went from not know what "integral" means to Putnam questions in like 2-3 months (thank you♥️)
Although I can kinda understand you, early on I couldn't really understand why he did a step, there are a couple of solutions to this but non are even coming close to touching the content on this channel:
1. First of all this channel (in my humble opinion) is to people who already had some experience with integrals, instead there are TH-camrs who explain every step in the process and teach methods, I recommend pairing this channel with some others and not committing the mistake of starting of with this stuff like I did.
2.I personally think this channel is plenty enough, if he wants *Integrals for you* can make another channel using your suggestion BUT NOT change the content on this channel, but no pressure this channel is amazing as it is!
Once again thanks for everything!🫡
@@gabyshavit8539 Ty for taking the time to write such an insightful response man. I appreciate it 👍
*But I think u may have misunderstood me regarding commentary* :
I'm suggesting commentary cuz otherwise the vids seem boring with such silence persisting throughout everywhere. Commentary is needed so viewers feel that there is indeed someone there who's doing the things and making an engaging atmosphere. It arouses interest.
If one is just dead silent, the vid will seem plain and boring & like some AI just printing out the answer to u without any interest.
Commentary for the steps was only a part of it. Commentary is needed as an intro, for engagement, and outro for ANY vid. It gives rise to engagement & attention, which are vital to make viewers stay, watch and take time to comment. Otherwise they wouldn't feel they're watching a youtuber but some supplement college vid. They wouldn't feel a part of the production of a content creator, but only a viewer of some random vid.
*Hence commentary is vital to increase views and comments.*
Many math youtubers like bprp & peyam have more viewership cuz of commentating and making a fun atmosphere while teaching. So, this channel too should do the same.
@@Gust52Thank you for the response!
I got your point now, the thing is adding commentary to this channel will just kinda mess with what is on it because part of the learning process of integrals at least in my opinion is doing it yourself, adding commentary may be nice but it shouldn't be to this exact channel, instead maybe a new channel for this will work but this style of content on this channel at least for me feels more engaging, if you find yourself watching the videos in boredom you can try to make it more interesting by actually trying to solve the integral yourself especially if it is a hard one, just not changing the style on this channel it really helped me learn fast and achieve mastery of integrals really fast and I know there are some other people who did too.
Anyway I understand you the content doesn't work for anyone, but in my opinion this is the best way to learn integrals really quick for anyone but only after having a nice base of them or else you're gonna have a hard time.
Hi I searched on your website for the integral of arctanx/x a while ago and after watching this video I got reminded of it, have you ever done this integral?
because I couldn't solve it in the end just thought it's a nice challenge
Hi! The integral of arctan(x)/x is a non-elementary integral, it cannot be expressed in terms of finite standard functions... However the integral of arctan(x)/x^2 can be integrated 😉
@@IntegralsForYou thanks it nice to know it's not a skill issue, well I can also assume the integral of ln(x+1)/(1+x^2) aka the integral of ln(tanx+1) (without bounds) has the same issue right?
@@gabyshavit8539 Yes, the integrals of ln(x+1)/(1+x^2) or ln(tan(x)+1) are also non-elementary... 🥲 If we had bounds maybe we could integrate it but I don't know how to
@@IntegralsForYou How do you even know if an integral is non-elementary?
@@gabyshavit8539 Because in general we need the derivative multiplying the functions you asked, or maybe something similar. For the case of ln(x+1)/(1+x^2) we see that there is no derivative multiplying anything so the only possible way is doing it by parts. When I do parts I see that it is impossible to continue... maybe also by my experience. After these checks, I can be wrong but I am 95% sure it is a non-elementary integral.