i solved this by factoring the denominator into x^2 terms and doing partial fractions to get a couple inverse tangent integrals. a bit messy but it led to some nice applications of euler’s formula and hyperbolic trig functions
This reminds me of the integral of 1/x^n+1, as an anti-derivative,, we can use our knowledge of complex numbers to decompose the polynomial into the product of (x-e^i-2pi/n) which actually for even n, we'll end up with (x^2-cos(2pi/n)x+1) since the roots come in conjugate pairs, so essentially we’ll end up with a partial fraction decomposition and a bunch of easy integrals… I have no idea how this is relevant but it’s interesting! KEEP UP THE FIRE WORK ME BOI KAMAL Edit: I think it’s relevant because we can write the following as 1/(x^2-e^2pi*i/5)( (x^2-e^-2pi*i/5))
There is an general form of this integal solving by ramanujan's master theorem we can drive this integral and do partial dirrivatives to look more harder
When I saw that 2/5ths pi in the thumbnail I thought, something golden is gonna pop up in that before its over.
same
Isn't the coefficient of x² in the integral just negative of the other root of x² = x+1 besides phi.
Thank you for this nice integration solution. I learned also about how to visualize the problem to solve.
i solved this by factoring the denominator into x^2 terms and doing partial fractions to get a couple inverse tangent integrals. a bit messy but it led to some nice applications of euler’s formula and hyperbolic trig functions
Hi,
"terribly sorry about that" : 1:17 , 2:05 , 2:46 , 4:22 , 4:50 , 6:22 ,
"ok, cool" : 2:38 , 5:22 .
This reminds me of the integral of 1/x^n+1, as an anti-derivative,, we can use our knowledge of complex numbers to decompose the polynomial into the product of (x-e^i-2pi/n) which actually for even n, we'll end up with (x^2-cos(2pi/n)x+1) since the roots come in conjugate pairs, so essentially we’ll end up with a partial fraction decomposition and a bunch of easy integrals… I have no idea how this is relevant but it’s interesting! KEEP UP THE FIRE WORK ME BOI KAMAL Edit: I think it’s relevant because we can write the following as 1/(x^2-e^2pi*i/5)( (x^2-e^-2pi*i/5))
Very nice solution.
Beautiful and delicious integral thanks for video!!
There is an general form of this integal solving by ramanujan's master theorem we can drive this integral and do partial dirrivatives to look more harder
Innovative solution. Thanks.
Love the recent videos!
Great video i hope for more in the future
Beautiful integration ❤❤❤
The thumbnail said x, not x² 😢
I noticed that also
Clickbait, lol
The thumbnail has been fixed. :)
@@heinrich.hitzinger 😂 nice save 👍
Wonderful video, but (dear Mr. RUclips) why the automatic dubbing?
Heyy broo friend from Sri Lanka ❤🎉
I thought the hardest part of this video was gonna be determining the cosine of 2π/5 from scratch.
bro, what app are you using?
@@algoboi Samsung notes
Got a nice integral problem as dinner, i like!
cos72=(√5-1)/4..dovrei fattorizzare il denominatore...
Very tasty, I like!