Has it been proven that the antiderivative (indefinite integral) of sinx/x does not exist?

[Random Variable]

One of my old calculus textbooks says that you can prove that the sinx/x doesn't have an antiderivative. But I have had teachers say that we just don't know how to take the antiderivative of sinx/x. Someone else told me that you can find the antiderivative by using complex variables (but he might have just been high on crack).

 

[akubi]

you express it in terms of a power series

 

[Random Variable]

Originally posted by: akubi
you express it in terms of a power series

That's cheating.

 

[akubi]

that's how it's done, SON.


ooooooooooooooh

 

[Random Variable]

Originally posted by: akubi
that's how it's done, SON.


ooooooooooooooh

Ok, but that just gives you a way to approximate the definite integral. It doesn't give you an antiderivative. And don't call me SON, son.

 

[RaynorWolfcastle]

Originally posted by: Random Variable
One of my old calculus textbooks says that you can prove that the sinx/x doesn't have an antiderivative. But I have had teachers say that we just don't know how to take the antiderivative of sinx/x. Someone else told me that you can find the antiderivative by using complex variables (but he might have just been high on crack).

Yes, it can be solved using complex variable calculus.

edit: I don't remember the specifics of it since it's been a few years since I took the class, but you had to do a path integral in the complex plane using Cauchy's theorem and subtract part of the path so that you're left with only the real portion

 

[akubi]

Originally posted by: Random Variable

Originally posted by: akubi
that's how it's done, SON.


ooooooooooooooh

Ok, but that just gives you a way to approximate the definite integral. It doesn't give you an antiderivative. And don't call me SON, son.

you editted your post from definite to indefinite after I replied

 

[Random Variable]

Originally posted by: akubi

Originally posted by: Random Variable

Originally posted by: akubi
that's how it's done, SON.


ooooooooooooooh

Ok, but that just gives you a way to approximate the definite integral. It doesn't give you an antiderivative. And don't call me SON, son.

you editted your post from definite to indefinite after I replied

An antiderivative is an indefinite integral not a definite integral. I made a mistake.

 

[Random Variable]

Originally posted by: RaynorWolfcastle

Originally posted by: Random Variable
One of my old calculus textbooks says that you can prove that the sinx/x doesn't have an antiderivative. But I have had teachers say that we just don't know how to take the antiderivative of sinx/x. Someone else told me that you can find the antiderivative by using complex variables (but he might have just been high on crack).

Yes, it can be solved using complex variable calculus.

You get some function as your answer?

 

[RaynorWolfcastle]

Originally posted by: Random Variable

Originally posted by: RaynorWolfcastle

Originally posted by: Random Variable
One of my old calculus textbooks says that you can prove that the sinx/x doesn't have an antiderivative. But I have had teachers say that we just don't know how to take the antiderivative of sinx/x. Someone else told me that you can find the antiderivative by using complex variables (but he might have just been high on crack).

Yes, it can be solved using complex variable calculus.

You get some function as your answer?

the integral from -infinity to infinity of sin(x)/x = pi. BTW, sin(x)/x is known as sinc(x) and is actually a very used function in electrical engineering because it is the Fourier transform of a square pulse

edit: I don't think this works for undefined integrals though and there were some formalisms about the way you went about it that I don't recall.

 

[dainthomas]

Originally posted by: Random Variable
One of my old calculus textbooks says that you can prove that the sinx/x doesn't have an antiderivative. But I have had teachers say that we just don't know how to take the antiderivative of sinx/x. Someone else told me that you can find the antiderivative by using complex variables (but he might have just been high on crack).

I do it all the time.

 

[DrPizza]

Originally posted by: Random Variable

Originally posted by: akubi
you express it in terms of a power series

That's cheating.

No, cheating is going to Wolfram and using the integrator
Of course, you don't get an answer there for that one

 

[Cooler]

Just use Itergration By parts hint to get you started X^-1 sin(x)

 

[Random Variable]

Originally posted by: DrPizza

Originally posted by: Random Variable

Originally posted by: akubi
you express it in terms of a power series

That's cheating.

No, cheating is going to Wolfram and using the integrator
Of course, you don't get an answer there for that one

Maple 10's answer is Si(x) (whatever that means)

 

[halik]

antiderivative? Is that was the kids are calling it nowdays?