Integrate ∫sin(sin(x)) dx - What is It?

[kahwawashay1]

What is ∫sin(sin(x)) dx ?

I was told that it was not an elementary function. Then what function is it?

 

[Dick]

What is ∫sin(sin(x)) dx ?

I was told that it was not an elementary function. Then what function is it?

I don't think it has a name yet. Do you want to name it?

 

[kahwawashay1]

I don't think it has a name yet. Do you want to name it?

Haha how can it not be already named? Can't someone solve it?

 

[SammyS]

Haha how can it not be already named? Can't someone solve it?

Solve what?

You've been told that it's not an elementary function.

About the best that can be done is to express the integrand as a Taylor series, the integrate that.

 

[Dick]

Haha how can it not be already named? Can't someone solve it?

Some integrals that can't be expressed as elementary functions are useful enough that they are given special names. E.g. http://en.wikipedia.org/wiki/Exponential_integral Not being able to 'solve' something doesn't it isn't useful or that there is nothing you can say about it.

 

[kahwawashay1]

Some integrals that can't be expressed as elementary functions are useful enough that they are given special names. E.g. http://en.wikipedia.org/wiki/Exponential_integral Not being able to 'solve' something doesn't it isn't useful or that there is nothing you can say about it.

ohhh
But I just downloaded Mathematica, and when I integrate sin(sin(x)), it gives me: (1/2)(sin²(x²))
But I can't see how taking the derivative of that gives sinsinx
Is Mathematica wrong then?

 

[kahwawashay1]

ohhh
But I just downloaded Mathematica, and when I integrate sin(sin(x)), it gives me: (1/2)(sin²(x²))
But I can't see how taking the derivative of that gives sinsinx
Is Mathematica wrong then?

Nvmmm I typed in the sin function in wrong format lol

 

[dextercioby]

And even the mighty Mathematica who knows the work of Gradsheyn and Rytzhik by heart couldn't do it...