# Integrate sin(sinx))

1. Dec 11, 2011

### kahwawashay1

What is ∫sin(sin(x)) dx ?

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

2. Dec 11, 2011

### Dick

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

3. Dec 11, 2011

### kahwawashay1

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

4. Dec 12, 2011

### SammyS

Staff Emeritus
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.

5. Dec 12, 2011

### Dick

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.

6. Dec 12, 2011

### kahwawashay1

ohhh
But I just downloaded Mathematica, and when I integrate sin(sin(x)), it gives me: (1/2)(sin2(x2))
But I cant see how taking the derivative of that gives sinsinx
Is Mathematica wrong then?

7. Dec 12, 2011

### kahwawashay1

Nvmmm I typed in the sin function in wrong format lol

8. Dec 12, 2011

### dextercioby

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