I have an integral multiple choise qustion in my calculus test, (I am studying engeneering)

[vaggelis]

Our professor has given us a math test and he didn't give any solving formula for a certain type of problems. I have scattered the internet, ask students from previous years for help to find the correct answer but for one problem (we had a lot) we cannot seem to understand how we can come to a certain conclusion. So I would be grateful if you could help. Anyway, he asks; "with the correct use of transformation the given integral; [math]\int \frac{1}{\sqrt{x+2-\sqrt[3]{x+2}}}dx[/math], can be also written as;". The given choices are the following;

Thank you in advance for your help and my apologies for any mistakes, english is not my native language.

 

[Deleted member 4993]

Our professor has given us a math test and he didn't give any solving formula for a certain type of problems. I have scattered the internet, ask students from previous years for help to find the correct answer but for one problem (we had a lot) we cannot seem to understand how we can come to a certain conclusion. So I would be grateful if you could help. Anyway, he asks; "with the correct use of transformation the given integral; [math]\int \frac{1}{\sqrt{x+2-\sqrt[3]{x+2}}}dx[/math], can be also written as;". The given choices are the following;
View attachment 30715
Thank you in advance for your help and my apologies for any mistakes, english is not my native language.

[math]\int \frac{1}{\sqrt{x+2-\sqrt[3]{x+2}}}dx[/math]
You have NOT shown one line of original work - but you want help for your TEST.

Your instructor has done a commendable job of finding a problem whose solution is not on internet.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

Think how you could factorize the denominator.

 

[BigBeachBanana]

Think about the domain of the integrand. It will give you an intuitive reason why the integral must be split into two parts.

 

[Dr.Peterson]

Our professor has given us a math test and he didn't give any solving formula for a certain type of problems. I have scattered the internet, ask students from previous years for help to find the correct answer but for one problem (we had a lot) we cannot seem to understand how we can come to a certain conclusion. So I would be grateful if you could help. Anyway, he asks; "with the correct use of transformation the given integral; [math]\int \frac{1}{\sqrt{x+2-\sqrt[3]{x+2}}}dx[/math], can be also written as;". The given choices are the following;
View attachment 30715
Thank you in advance for your help and my apologies for any mistakes, english is not my native language.

Evidently ethics is not your native language, either. Nor is learning. I wouldn't want to use anything you design in the future.

But if you would like to actually learn something, and earn credit, what sort of substitution might you want to try?

 

[vaggelis]

Our professor has given us a math test and he didn't give any solving formula for a certain type of problems. I have scattered the internet, ask students from previous years for help to find the correct answer but for one problem (we had a lot) we cannot seem to understand how we can come to a certain conclusion. So I would be grateful if you could help. Anyway, he asks; "with the correct use of transformation the given integral; [math]\int \frac{1}{\sqrt{x+2-\sqrt[3]{x+2}}}dx[/math], can be also written as;". The given choices are the following;
View attachment 30715
Thank you in advance for your help and my apologies for any mistakes, english is not my native language.

Since a lot of people are way to concerned to jump into conclutions rather than provide any constructive help I want to clarify a few things. I never asked you to just tell me the answer, I only gave you the photo with the answers so that you have an idea of what is going on with that problem because you wouldn't understand a thing if I just told you only what it was given.

If you could actually read what I am writting in the thread is that our professor DID NOT give any type of formula, example not even a course for these type of questions. So we have to come up with the solutions out of thin air. For those who are telling me that I did not show you not even a line of original work, please answer me how the **** am I going to provide you with any type of math work that are not gibberish to a problem that I have no idea how to even start. That is because as I said the professor did not care or did not remember if we did anything similar to this. Why you may ask? Well I have the same question as you. Also dont start telling me to email him because I have and he didnt respond. Believe me if only I had a clue of how to start this thread would not have existed.

However because I am not the type of person who just expects people to give him the answer I did try at least a few things (NO WAY) by what I saw in books and notes from students of previous years that actually did have questions like those tought. So I am posting them as well to give you the work that you need (I dont know if you would understand a lot of things because they are written in greek). Now that you know that I actually want to learn something and just start from anywere I would apreciate any constructive type of help.

P.S. To explain the file a little, the second page is a formula that I found and the first one is what I could do based on that. Also many of you would propably say that this work is too little but I am only posting this because this is the only thing that I actually did came up with anything than trying certain stuff left and right that lead nowhere. In sort that is the only non gibberish math that I could do for this problem.

 

[vaggelis]

[math]\int \frac{1}{\sqrt{x+2-\sqrt[3]{x+2}}}dx[/math]
You have NOT shown one line of original work - but you want help for your TEST.

Your instructor has done a commendable job of finding a problem whose solution is not on internet.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem.

Think how you could factorize the denominator.

As I said there is not much I can provide you with when I do not know how to start, this is not high school math. Anyway, I posted a formula that I found that could be of help for this problem and what I did based on that. If you have any type of formulas that are somehow link to those type od problems I would apreciate if you could share them. Also our intructor did a commendable job of finding a problem that he did not show anything similar to it in class. That is why I am asking the internet.

 

[vaggelis]

Evidently ethics is not your native language, either. Nor is learning. I wouldn't want to use anything you design in the future.

But if you would like to actually learn something, and earn credit, what sort of substitution might you want to try?

I never asked you to tell me the answer, I aked for help, since I do not know how to start. I gave the answers because without them you would not have any idea of what is going on in the problem. Anyhow, I tried substitution of x+2=u but that doesnt do anything. I am pretty sure that this problem cannot be solved by substitutions that I can thing of on my own. They are most likely complicated ones that are given with formulas either by the proffessor ( which as I said in my reply below he gave none) or by books. I found nothing on books but I did find something of notes from previous students. I posted that so that you have an idea of what is propably needed. If you have any idea of formulas refering to these problems I would apreciate it. Again I want help not just the answer so yes dont be shocked I want to learn.

 

[vaggelis]

Think about the domain of the integrand. It will give you an intuitive reason why the integral must be split into two parts.

From what I can understand and have tried the spliting will occur after any substitutions I make. However I really cant find what substitution to make as I am sure that it is a complicated one and not something easy that I can thing on my own. What I am trying to say is that I am pretty sure that there are some formulas that I dont know of that tell me for those type of integrand what to substitude.

 

[Deleted member 4993]

As I said there is not much I can provide you with when I do not know how to start, this is not high school math. Anyway, I posted a formula that I found that could be of help for this problem and what I did based on that. If you have any type of formulas that are somehow link to those type od problems I would apreciate if you could share them. Also our intructor did a commendable job of finding a problem that he did not show anthing similar to it in class. That is why I am asking the internet.

Looking at the prospective solutions you should have asked "yourself":

what is (u-1)*(u^2 + u + 1) = ?

and

what is (u+1)*(u^2 - u + 1) = ?

did you? If you did - what did you find?

 

[vaggelis]

Looking at the prospective solutions you should have asked "yourself":

what is (u-1)*(u^2 + u + 1) = ?

and

what is (u+1)*(u^2 - u + 1) = ?

did you? If you did - what did you find?

Well I did not because I did not think that tweaking the answers of a problem is the right way to slove this. I did now to every answer (I attached a pdf file) and as you can see "c" answer have some things in common with the alternate form of the integrate in the file I posted in one of my replies. I also have some bad news, the formula that I sent you says that the integrate has solutions when only if ONE of the; ρ, (m+1)/n, ((m+1)/n)+ρ belongs to Z. I saw my notes and I made a mistake and none of them belong to Z. So this fomrula doesn't work with the alternave form that I came up with. So I am back again on ground zero.

 

[Deleted member 4993]

Well I did not because I did not think that tweaking the answers of a problem is the right way to slove this. I did now to every answer (I attached a pdf file) and as you can see "c" answer have some things in common with the alternate form of the integrate in the file I posted in one of my replies. I also have some bad news, the formula that I sent you says that the integrate has solutions when only if ONE of the; ρ, (m+1)/n, ((m+1)/n)+ρ belongs to Z. I saw my notes and I made a mistake and none of them belong to Z. So this fomrula doesn't work with the alternave form that I came up with. So I am back again on ground zero.

Please post screen-shots of your pdf files. I am not going to open any pdf file.

 

[vaggelis]

Oh ok. I just thought pdf would be easier

 

[Steven G]

I am sorry but I do not believe what you say when you say that you never solved such a problem like this before. You need to make a u-substitution, are you saying that you never were taught u-substitution?

One more thing--if you ever use profanity on this site again I will push for you to be banned. I could not care whether or not you spell out the profanity or not.

 

[AvgStudent]

If I were to guess, I would choose d because of the function's graph. Answer d has [imath]\int \frac{1}{u+1}=ln|u+1| + C[/imath], which is the only one that matches the right portion of the graph's domain. However, I'm unsure about the [imath]u^2-u+1[/imath]. The left portion sort of resembles a parabola. Also, from what I know, the integral is a non-elementary antiderivative, so I'm not sure how your professor transformed it into an elementary antiderivative that's integrable. So the best bet is to ask your professor directly. I'm curious as well.

 

[vaggelis]

I am sorry but I do not believe what you say when you say that you never solved such a problem like this before. You need to make a u-substitution, are you saying that you never were taught u-substitution?

One more thing--if you ever use profanity on this site again I will push for you to be banned. I could not care whether or not you spell out the profanity or not.

I am sorry for any bad words that I used I was just a little annoyed of the way people talked to to a person that they don't even know. Like I was some sort of a student who wants things solved by others, which I am not. I should have expect such type of reaction from the internet since people are prone to jump into conclusions. Anyway, of course we have learned a u substitution but as I addressed in every single of my replies this is not some sort of u substitution that you can come up with on your own. That is something that the person below you on the replies noticed. Its been given on formulas, books, notes ect. If you watch one of my pictures you will understand what type of formula I am talking to. This was the only reason why I posted this on the internet, if people were aware of any formula that fits to that problem that I am not since our professor didn't give any. If you believe or have thought of some simple substitution that can solve this problem I am extremely curious to see which one since I found none, so share it if you want. It doesn't matter anymore the quiz closed but I am just curious.

 

[nasi112]

The professor sometimes explains 3 or more lessons, and then she combine them in one question. When you first look at the question, you say oh my god, I have never seen or been taught this before, but when you divide the question into parts, you discover that you have learnt everything. I think that this is what happened to you.

 

[vaggelis]

If I were to guess, I would choose d because of the function's graph. Answer d has [imath]\int \frac{1}{u+1}=ln|u+1| + C[/imath], which is the only one that matches the right portion of the graph's domain. However, I'm unsure about the [imath]u^2-u+1[/imath]. The left portion sort of resembles a parabola. Also, from what I know, the integral is a non-elementary antiderivative, so I'm not sure how your professor transformed it into an elementary antiderivative that's integrable. So the best bet is to ask your professor directly. I'm curious as well.
View attachment 30738

Oh wow I really didn't expect someone to give a constructive help. So the correct answer was c, which I selected because if you see on one of my pictures I transformed this integral in to an alternative form which was closer to answer c. It is a horrible way to choose an answer but oh well. C also fits better because of the x-1 Which is more close to
(x+2-(x+2)^(1/2))^(1/2). There is no + between the two x+2 that's what I am trying to say. You have a great point about the elementary antiderivative and this was exactly why I couldn't quite get how to transform a root to elementary integrals. I will ask the professor because I am curious too but I am not sure when and if I find him because we have no courses left yet since the exams start in a week. Thank you again!

 

[vaggelis]

The professor sometimes explains 3 or more lessons, and then she combine them in one question. When you first look at the question, you say oh my god, I have never seen or been taught this before, but when you divide the question into parts, you discover that you have learnt everything. I think that this is what happened to you.

I really do hope that this is the case and I will ask him but I am fairly certain that it is not. That is because 2 other similar problems that I solved could only be solved by formulas that were given in students on previous years. Our professor did not gave them to us and those formulas seem to be the only ones that could solve those certain type of substitution problems. They tell you when you have a certain type of integral what exactly to substitute. The reason why they are given and they don't just let us think of them on our own its because they are complicated substitutions and you really really can't come up with it. I can sent you some pictures for you to see what formulas I am referring to and the problems that we had and were similar to it. Dont worry the quiz closed so I will not cheat or anything but i solved those problems anyway. The only left that could not really fit to any formula is the one I posted. Secondly every student on my class couldn't solve problems similar to this (the exam is 3 days long so obviously asking left and right is allowed), so for every student to be wrong is a little weird.

 

[nasi112]

I really do hope that this is the case and I will ask him but I am fairly certain that it is not. That is because 2 other similar problems that I solved could only be solved by formulas that were given in students on previous years. Our professor did not gave them to us and those formulas seem to be the only ones that could solve those certain type of substitution problems. They tell you when you have a certain type of integral what exactly to substitute. The reason why they are given and they don't just let us think of them on our own its because they are complicated substitutions and you really really can't come up with it. I can sent you some pictures for you to see what formulas I am referring to and the problems that we had and were similar to it. Dont worry the quiz closed so I will not cheat or anything but i solved those problems anyway. The only left that could not really fit to any formula is the one I posted. Secondly every student on my class couldn't solve problems similar to this (the exam is 3 days long so obviously asking left and right is allowed), so for every student to be wrong is a little weird.

Are you sure that there is no mistype in this integral? I have a doubt that your professor made a mistake. And there is another thought which is more logical that you made the mistake. If this integral is correct as well as the answers, then you mixed this problem with another problem's answers. Do you get what I mean?

 

[vaggelis]

So I have a little update for those who are curious (if any), a positive one. After deciphering the Da Vinci code of my professor I am fairly certain that he did not mean to write this derivative; [math]\int \frac{1}{\sqrt{x+2-\sqrt[3]{x+2}}}dx[/math] but he mean to write this; [math]\int \frac{1}{\sqrt{x+2}-\sqrt[3]{x+2}}dx[/math]About the second derivative I found again from notes of students of previous years that were given by the professor that were not given to us, this formula;



You can see on the second page that this formula worked and I very very easily concluded on the answer c of the given answers which is the correct one.
So you see that after all I wasnt some crazy lazy dude who wants the easy way and others to solve the problem for him. There was no correct answer for the derivative that he gave and thats why I asked for help, because i genually could not solve this because oh well as it turns out it could not be solved. So yeah it is my fault that I did not think firstly about what derivative our professor really wanted to write but I am really not surpised because that happens a lot on his tests.
Anyhow, consider this matter solved and you will not hear from me again since after all I am not a very ethical person for asking help on the internet about problems that I am stuck to. I hope that next time you will not judge someone so easily and provide constructive criticism and not just the classic "You are not ethical for requesting help and your professor is correct".

Thank you all for any form of help that you gave me.