The integral ∫sin(sin(x)) dx is confirmed as a non-elementary function, meaning it cannot be expressed in terms of elementary functions. Participants in the discussion noted that while Mathematica provides a result, it may not accurately represent the integral due to input errors. The best approach to handle such integrals is to express the integrand as a Taylor series and integrate that series. This integral does not have a widely recognized name, highlighting its complexity and the ongoing exploration in mathematical functions.
PREREQUISITESMathematicians, calculus students, and anyone interested in advanced integration techniques and the study of non-elementary functions.
kahwawashay1 said:What is ∫sin(sin(x)) dx ?
I was told that it was not an elementary function. Then what function is it?
Dick said:I don't think it has a name yet. Do you want to name it?
Solve what?kahwawashay1 said:Haha how can it not be already named? Can't someone solve it?
kahwawashay1 said:Haha how can it not be already named? Can't someone solve it?
Dick said: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 said: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?