@polymathematic: An integral connection between the natural log and the golden ratio phi. Do people want more calculus?

Tim Ricchuiti
Tim Ricchuiti
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Region: US
Wednesday 20 December 2023 20:08:55 GMT
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dontworryillgofirst
Alejandro The Great :
my ability to believe the expression we get back here is severely hindered by the fact I don't understand any of this
2023-12-20 20:31:10
253
surgataz
Surgataz :
I used to resolve problems like this for breakfast, but then I became a software developer and now this sounds like …somebody that I used to know…
2023-12-20 23:58:36
168
cosmicowlboi
Tik Toker :
what level maths would this be??
2023-12-20 20:23:16
59
tlys03
tlys :
Alternatively you can trig substitute with i*sin(t) then you get the indefinite integral as sinh^(-1)(x) :) sinh^(-1)(1/2)=ln(ϕ)
2023-12-20 23:27:29
39
retrobate
David T :
“Phee”? Thought it was “Phie” (like “lie”)? 😁
2023-12-20 23:57:20
16
cianphysics
The Irish Physicist :
I would just see that this integral is the derivative of Sinh^-1(x) and you can sub in
2023-12-20 21:11:04
12
dillydallard
dillydally :
I immediately thought of the hypotenuse of a triangle. Tangent because you can do O/A which you can make x*2
2023-12-20 20:29:53
12
carlosvl_1510
CarlosVL_1999 :
now I miss integral calculus instead of learning Navier Stokes equations
2023-12-23 00:17:01
6
mxttwestermxn
matt :
Would the sqrt(sec^2(u)) not become |sec(u)| instead of cancelling out?
2023-12-21 12:43:15
6
__epo__
epo :
getting cal 2 flashbacks
2023-12-21 08:41:43
5
asianexcellence2215
Brian➗ :
@Nahian Khair @shadab @Koolguy pretty easy
2023-12-23 08:58:06
4
cluntyqueen1
🧀👸🏼 :
i thought i was good at math until i took calc 🤪
2023-12-21 16:55:07
4
yungmaplefan
yungmaplefan :
Took one look at the equation and got war flashbacks
2023-12-21 07:19:02
4
naflodi
naflodi :
I understand but I shouldn’t
2023-12-21 03:51:10
4
usersx2ijyryif
︎ :
I plugged into a calculator and it gave me the answer as inverse of hyperbolic sine of 1/2 which had me thinking why that's equivalent to ln((1+√5)/2) and I found the answer sinh(x)=(e^x-e^(-x))/2
2023-12-20 22:18:39
4
billrobbers
Billy Bob :
when I saw no trigonometric functions in the original but then trigonometric functions came anyway 😭
2023-12-20 21:40:42
4
oshaneballoun
O.Shane Balloun :
♥️So elegant.
2024-01-08 11:04:11
3
applepizzazz
FermatsFirst :
I could never have solved this myself, but I'm very proud of the fact that I completely followed every step, even tho I haven't done calc in 40+ yrs.
2023-12-29 04:26:16
3
theromanempire1923
Roman (Yuno Miles’ Version) :
Yeah that’s what I was thinking too
2023-12-21 06:00:29
3
zainn150
Zain :
hyperbolic sub
2023-12-21 00:14:05
3
youkaihenge
Nick Stark :
Apply Feynmann's Technique makes this much easier
2023-12-20 22:08:17
3
its_katie_l0l
Katie Kennedy :
what job would let me do this all day every day?
2023-12-20 20:52:16
3
reutlingen91
reutlingen91 :
Beautiful 😻
2023-12-20 20:47:50
3
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