#Medium Level Integral

79 messages · Page 1 of 1 (latest)

gray sleetBOT
signal lodge
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@open hinge Honestly not sure, but I think the first step would be to see if you can rewrite the integrand in a simpler way.

Usually with infinitely nested functions, you set the entire thing equal to y, and get something like y = (a function of x and y), and see if you can solve for y.

Not entirely sure though

open hinge
signal lodge
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If y = ln(x + ln(x + ...), then y = ln(x + y)

open hinge
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ah i see

signal lodge
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Not sure what useful results that can give you honestly, but that was my first attempt

open hinge
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then what next?

signal lodge
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I was going to suggest solving for y, but that's not very easy here. That's where I got stuck for this

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Idk if the lambert W function or that weird thing is needed here

open hinge
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WHAT

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I dont even learn lambert 😭

signal lodge
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Yeah I just learned that from watching random youtube videos. It's not something I think people should be expected to know honestly

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Is this a calc 2 class?

open hinge
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its from Daily Integral website

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search it up

signal lodge
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ah - i have no idea what they're expecting then

open hinge
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some qns can be really nasty

signal lodge
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it looks kinda like an interesting problem

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you struggling with it? I certainly am lol

open hinge
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same

west gate
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y = this thing

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looks similar to a recursive thingy i saw earlier

signal lodge
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that's what i thought, but then y = ln(x + y) and then what

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e^y = x + y isn't solvable algebraically

west gate
west gate
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it's joever

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another method might be needed

runic talon
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Yo

signal lodge
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my last attempt would be just to set u = integrand and see what happens lol

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wait: this would like to implicit differentiation in a u-sub - that's kinda funny

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shoot am i really going to do math when i don't need to?

runic talon
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Im trying solving by putting x+ln....=y and chaning integral accordingly

west gate
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y = x + lny

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e^y = e^(x + lny)

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e^y = e^x * y

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ok wow

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yeah this works lol

signal lodge
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i think y = ln(x + y)

west gate
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use y = x + ln...

signal lodge
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and then integrand is ln(y)? That's an interesting idea

west gate
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all that's left might be knowing the integral of W()

signal lodge
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yeah, for me that's a little silly to expect, but i guess they aren't meant to be friendly integrals

west gate
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that was pretty tricky

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the author probably knew we'd use like y = ln...

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and made it a bit harder

signal lodge
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they got me with that lol

west gate
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pretty neat

signal lodge
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i didn't get it

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i'll try it that way

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y = -W(-exp(-x))?

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i couldn't be bothered trying to integrate W(x), but whatever

runic talon
signal lodge
# open hinge same

how'd you find that math site? it's pretty cool - like wordle but for math

open hinge
signal lodge
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nice

open hinge
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someone was talking about this

signal lodge
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the problems are kinda tricky, idk if it's something i want to dump that much time/effort into, am lazy

runic talon
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Idk i give up

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🏳️

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@open hinge what's website

signal lodge
open hinge
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Daily Integral

signal lodge
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wow i figured that out

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i'm kinda surprised you don't need to know about integrating W(x) to do that

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@open hinge Did you want the solution?

west gate
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good daily exercise

atomic topaz
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u dont need W(x)

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its solvable using elementary stuff

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and its solvable using y= ln(x+y) .. instead of what u guys came to conclude that is y = x + ln y

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u had to change the integral wrt to X to wrt Y and its pretty straight forward after that

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catbit this website is cool.. lol thank u OP for postin this

open hinge
scarlet prism
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this recurisive tpe of shit

wet condor
errant remnant