Finding tha antiderivate

[Aedrha]

Hi there!
This is my first post, also english is not my first language. I hope i can come acrosse somewhate clear how ever.
I am studying a course in single varible calculus and I am well and truly stuck.



I am supposed to find the antiderivate here. Honesty i quite don't know what do here. This particulare form of function is not present anywhere with regards to antiderivates in our litterature so I'm flying blind.

My first thought was to factorize the function.



My plan here was to integrate by parts so:


and then:



I tried to do the integration by parts the other way around but it did'nt turn out any better. I also tried to substitute sqrt(X²+1) and sqrt(x) but i could'nt make heads or tails of it.

Is there some method to finding the anitederivate of functions like this?

Any help is greatly appriated!

Thanks!

 

[Deleted member 4993]

Hi there!
This is my first post, also english is not my first language. I hope i can come acrosse somewhate clear how ever.
Anyway I am well and truly stuck.

[MATH][/MATH]

You did NOT POST a problem!!

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.

 

[Aedrha]

You did NOT POST a problem!!

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.

Forgive me, i accidently clicked post instead of preview. I found no way of removing the post. There should be a problem now.

 

[Dr.Peterson]

Hi there!
This is my first post, also english is not my first language. I hope i can come acrosse somewhate clear how ever.
I am studying a course in single varible calculus and I am well and truly stuck.


View attachment 25879
I am supposed to find the antiderivate here. Honesty i quite don't know what do here. This particulare form of function is not present anywhere with regards to antiderivates in our litterature so I'm flying blind.

My first thought was to factorize the function.

View attachment 25880

My plan here was to integrate by parts so:

View attachment 25881
and then:


View attachment 25882
I tried to do the integration by parts the other way around but it did'nt turn out any better. I also tried to substitute sqrt(X²+1) and sqrt(x) but i could'nt make heads or tails of it.

Is there some method to finding the anitederivate of functions like this?

Any help is greatly appriated!

Thanks!

You have nicely shown work (apparently after you were asked to). When you say, "Honesty i quite don't know what do here", that isn't really true, as the thing to do is what you are doing, trying different methods. I don't look at it and instantly see the best method, any more than you. I would do some of the same things. (I would never start as you do for parts, though -- I look for the easy ways first.)

But because nothing I see works, I went to WolframAlpha and it gives an answer using a "hypergeometric function". That suggests it can't be done by methods you or I have learned. It can be wrong, but the natural thing now is to ask whether you might have miscopied the problem, or omitted something? Please show us the entire problem as given to you (even in another language) so we can see if there is something subtle in the way it is written.