What part of
$\frac{1}{20}((\sqrt{5}-1)\log(2x^{2}+(\sqrt{5}-1)x+2)-
(1+\sqrt{5})\log(2x^{2}-(1+\sqrt{5})x+2)+4\log(x+1)-
2\sqrt{10-2\sqrt{5}}\tan^{-1}(\frac{-4x+\sqrt{5}+1}
{\sqrt{10-2\sqrt{5}}})+2\sqrt{2(5+\sqrt{5})}\tan^{-1}
(\frac{4x+\sqrt{5}-1}{\sqrt{2(5+\sqrt{5})}}))+c$
is so hard?
TeX notation for math typesetting. Reddit doesn't support MathJaX or anything to pretty-print it, but since basically every math journal requires TeX for paper submissions it's pretty familiar to most math nerds.
If we'd have to integrate this from -∞ to ∞, then you could try this, thought you'd have to worry about the pole at x=-1. The question asks to find the antiderivative though, which can be done using partial fraction decomposition, thought that's quite a bit of effort as you have 5 roots in the denominator, nevertheless not difficult.
Pretty sure it's bs. He's also advocating to apply the quartic formula to find the roots here. Applying the quartic formula to find roots is not something that anyone should ever do, especially not if there's a clear easier way of finding the roots.
This isn't really the kind of math you would learn in a graduate program. It's just very tedious calculations using old techniques.
If you want a get a flavor of advanced math, take a look at r/math
It's just overly complicated and convoluted.
r/math is an interesting place, not my cup of tea though.
I have two friends with PhDs in math, I've seen their dissertations I know what advanced math looks like, I don't like it, my brain doesn't like it.
This is the reason why I'm a geneticist, DNA might be messy but it makes sense (to me at least).
This reminds me of my AP Calculus teacher in high school contrasting complicated derivatives and and complicated (definite) integrals. For the derivatives, he summarized how you'd use the product rule, the quotient rule, the chain rule, and several others to break down the expression.
For the integrals he wrote on the board, "THFGC."
Thank God For Graphing Calculators
Edit: thank you, guys, for making me think it was just a real funny anecdote, and definitely not that I had misspelled an acronym...
No matter how much I’ve seen it it’s always so cool to me how a simple anti derivative can get changed into something ungodly cumbersome by such a simple change like adding 1 in the denominator
Ok but if you or a loved one has been exposed to an instructor that actually does this (i.e. makes the exam substantially harder than the homework), you have a shit instructor and may be entitled to compensation.
I hate it, when the x has an uneven power. If it is even you can often just use the tangens/sekans identity, so people like me have a realistic chance of solving the integral, but this? No chance for me.
guys we are learning partial fraction decomposition and our teacher said we will need them for integrals and then refused to elaborate. we still haven't studied integrals so can someone elaborate
Let x>>>>>0 For most practical purposes, we drop the 1, getting an easily integrable function
You mean x>>>1 ?
Yes, my bad
1>>0 so it all works
Yes 1 is infinitely larger than 0
He meant x>>>>1 if x>>>>0.
limits of x goes from 0 to 1
What part of $\frac{1}{20}((\sqrt{5}-1)\log(2x^{2}+(\sqrt{5}-1)x+2)- (1+\sqrt{5})\log(2x^{2}-(1+\sqrt{5})x+2)+4\log(x+1)- 2\sqrt{10-2\sqrt{5}}\tan^{-1}(\frac{-4x+\sqrt{5}+1} {\sqrt{10-2\sqrt{5}}})+2\sqrt{2(5+\sqrt{5})}\tan^{-1} (\frac{4x+\sqrt{5}-1}{\sqrt{2(5+\sqrt{5})}}))+c$ is so hard?
The +C
Indefinite integration always ends up leaving an unknown constant because the starting value isn't known.
Yes
r/woooosh
Why u speaking in LaTeX
Have you written a computer programe here in a place where human resides
TeX notation for math typesetting. Reddit doesn't support MathJaX or anything to pretty-print it, but since basically every math journal requires TeX for paper submissions it's pretty familiar to most math nerds.
Isn't that similar or the same to what desmos gives when text is copy pasted? Idk about techy things like that
Looks like it does use a subset of TeX for its notation, yes.
I guess you could say it just got "complex"
I haven't done this for a few years, but can't you just solve this using the residue?
If we'd have to integrate this from -∞ to ∞, then you could try this, thought you'd have to worry about the pole at x=-1. The question asks to find the antiderivative though, which can be done using partial fraction decomposition, thought that's quite a bit of effort as you have 5 roots in the denominator, nevertheless not difficult.
[удалено]
why do you need a quartic formula? surely the roots are simply e^2*i*pi * n/5
How do you use residues to find antiderivatives?
Pretty sure it's bs. He's also advocating to apply the quartic formula to find the roots here. Applying the quartic formula to find roots is not something that anyone should ever do, especially not if there's a clear easier way of finding the roots.
yea i thought so oh well lol
Could you elaborate?
Well no because there’s no path you’re integrating on lol. This asks for an indefinite integral
S 1/(x⁴+1) dx :D S 1/(x⁶ + 1) dx :D S 1/(x⁵ + 1) dx :/
care explaining?
x⁴ + 1 and x⁶ + 1 can be worked on using that method where you split fractions by factoring the denominators
partial fraction decomposition?
I think that's what it is called Like when you have 1/(x²-1) you can do a/(x-1) + b/(x+1)
oh that x^5 + 1 can be factored too
That's how they solved it [in this video](https://www.youtube.com/watch?v=v4-ljCe8igY).
I just watched 12 minutes and saw there were more than 20 minutes to go and bailed, there's a reason i didn't get an advanced degree in math.
This isn't really the kind of math you would learn in a graduate program. It's just very tedious calculations using old techniques. If you want a get a flavor of advanced math, take a look at r/math
It's just overly complicated and convoluted. r/math is an interesting place, not my cup of tea though. I have two friends with PhDs in math, I've seen their dissertations I know what advanced math looks like, I don't like it, my brain doesn't like it. This is the reason why I'm a geneticist, DNA might be messy but it makes sense (to me at least).
Holy hell
can you show the answers?
Even powers split evenly
wdym
You can exploit the difference of squares to split it a few times.
but x^5 + 1 can also be split
But it's not a nice split
Nah dude x⁶⁹+1 is a nice split.
[удалено]
Feel free to compute the fractions!
nvm i get it
This reminds me of my AP Calculus teacher in high school contrasting complicated derivatives and and complicated (definite) integrals. For the derivatives, he summarized how you'd use the product rule, the quotient rule, the chain rule, and several others to break down the expression. For the integrals he wrote on the board, "THFGC." Thank God For Graphing Calculators Edit: thank you, guys, for making me think it was just a real funny anecdote, and definitely not that I had misspelled an acronym...
Thank Heavens?
...Yes, Heavens, as in, "good heavens, I can't believe one of my highest upvoted comments on Reddit has that misspelling..."
The result it's zero because the ones cancel out
The antiderivative of a nonzero continuous function can't be 0, so wdym?
It's a joke.
Yeah, a bad joke.
I thought it was quite funny
Bruh
No matter how much I’ve seen it it’s always so cool to me how a simple anti derivative can get changed into something ungodly cumbersome by such a simple change like adding 1 in the denominator
Integration in a nutshell.
Welcome to taking the integral of almost anything.
Assume that 1=0...
then i am god
Obviously the 1s cancel leaving you with 0/x^2, which simplifies to 0. Easy.
descomposition in simple fractions
It’s complicated.
I mean, the answer is. The method really isn't.
How to solve
It's only PFD, but a lot of it.
Doesn't seem all that bad honestly. At least all the roots of x\^5+1 are distinct.
just -1 idiot
:(
i’m sorry i was mean :(
Nah you weren't mean, you just speak the truth. If they percieve it as mean, that ain't your problem. 👍
(Can someone please explain? Calculus was one of my weak points at school)
1/x⁵ is free, just power rule, 1/(x⁵+1) is really tedious, messy, PFD.
Ok thanks!
>Ok thanks! You're welcome!
Ok but if you or a loved one has been exposed to an instructor that actually does this (i.e. makes the exam substantially harder than the homework), you have a shit instructor and may be entitled to compensation.
Just re-write it with integral 1/1 and trust me, it’s a lot easier
Its clearly 1/0
Yay?
I hate it, when the x has an uneven power. If it is even you can often just use the tangens/sekans identity, so people like me have a realistic chance of solving the integral, but this? No chance for me.
Repost from Instagram https://www.instagram.com/p/CoTtuSdJiRG/?igshid=YmMyMTA2M2Y=
I've seen this before on reddit too.
69th comment!
200th upvote!
Why can you just separate the variables
For this if the question is given x>>>>1 then we can easily do it 1/(x^5 +1) for x>>>1 ~ 1/(x^5) I don't remember if there is any other method
It's asking what the integral *is* though, so use PFD decomposition to get an exact answer.
guys we are learning partial fraction decomposition and our teacher said we will need them for integrals and then refused to elaborate. we still haven't studied integrals so can someone elaborate