hey bro, i was thinking bout the expression, and thought maybe we can apply binomial theorem. since the numerator is 1, does that mean the expansion will have negative powers? idk if i’m on the right track tho, would love to hear ur thoughts!
Hello, the generalized binomial theorem would work to give you a solution in the form of a series. You would integrate the series for (1+x^2)^(-n). The series (which works for any complex n) for that function begins as follows: 1+(-n)x^2+(-n(-n-1)/2!)x^4+(-n(-n-1)(-n-2)/3!)x^6+… Edit: The above series converges for |x|1 can be obtained by factoring out x^(-2n) and finding the series for (1+1/x^2)^(-n) which will have negative powers in this case.
@hadirihawi ayyyy !!!! i just realized i havent studied binomial theorem yet, i thought i did 🥹, i was confusing it with the basics of polynomials i’m learning now (like adding, subtracting, and simplifying them), so i got a little mixed up with the concepts. thanks for your help and patience! 🎀
@@hadirihawi yea ur totally right! i got mixed up between binomial theorem n simplifying polynomials, i realized i havent studied binomial theorem yet "im still in 9th grade", ill actually learn it in 2nd year of high school. sorry if i confused u with my question! and ur right bout the negative exponent, it’d make the expression negative, not positive like i thought.
I do have the full solution for all natural n in my linktree under the “all-in-one integrals” link. The general method is to perform a partial fraction decomposition and so the final answer will be a combination of logarithms and inverse tangents.
Usually, a challenge is difficult. But on a serious note, this is the basis of all of my shorts, where I do compute various roots up to at least 5 decimal spots.
Yeeeeaaaah I'm cooked, roasted and Burned.
Finally not numerical/approximation 🥰
i love the end
How did you derive the quartic formula? Explain please!
You could also use beta function to solve this
Moment vierre cloud☠️
hey bro, i was thinking bout the expression, and thought maybe we can apply binomial theorem. since the numerator is 1, does that mean the expansion will have negative powers? idk if i’m on the right track tho, would love to hear ur thoughts!
Hello, the generalized binomial theorem would work to give you a solution in the form of a series. You would integrate the series for (1+x^2)^(-n). The series (which works for any complex n) for that function begins as follows: 1+(-n)x^2+(-n(-n-1)/2!)x^4+(-n(-n-1)(-n-2)/3!)x^6+…
Edit: The above series converges for |x|1 can be obtained by factoring out x^(-2n) and finding the series for (1+1/x^2)^(-n) which will have negative powers in this case.
@hadirihawi ayyyy !!!! i just realized i havent studied binomial theorem yet, i thought i did 🥹, i was confusing it with the basics of polynomials i’m learning now (like adding, subtracting, and simplifying them), so i got a little mixed up with the concepts. thanks for your help and patience! 🎀
@@hadirihawi yea ur totally right! i got mixed up between binomial theorem n simplifying polynomials, i realized i havent studied binomial theorem yet "im still in 9th grade", ill actually learn it in 2nd year of high school. sorry if i confused u with my question! and ur right bout the negative exponent, it’d make the expression negative, not positive like i thought.
Nice video!
Keep going ❤
this is awsom
now can u explain how to do the indefenit interal of 1/x^n+1
as u did
thxx
oh hell nah
I do have the full solution for all natural n in my linktree under the “all-in-one integrals” link. The general method is to perform a partial fraction decomposition and so the final answer will be a combination of logarithms and inverse tangents.
@@hadirihawi okayy
I don't know how to do that. How cooked am I?
Pretty cooked, drop out.
Pretty cooked, drop out.
if you haven't taken complex analysis, then you're fine
You're so handsome ❤ I can't focus on your lecture 😂
i have a challenge for you calclulate a sqrt of two special case and general case for any positive integer
Usually, a challenge is difficult.
But on a serious note, this is the basis of all of my shorts, where I do compute various roots up to at least 5 decimal spots.
This notation of 'Contour integral over something' is illegal in MS Word.
Gamma of n is (n-1)!
Bro please can you solve sqr(x/1-x) +sqr(1-x) =5/2
Pls approximate 12|22412 (divide)
Majority of us just didn't understand right?😂
ARE YOU FALLING IN LOVE 🎶
am i tripping or n is a complex number ?
I’ve chosen to show this for n complex, yes. This only presents an issue when I need to take derivatives to obtain the residue.
Hello😊
Bruh
Umm hi
ㅤ