Integrating Sin(x^3) - Homework Equations & Solution

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Homework Statement


I need to intergrate sin(x^3) for a sum and I don't know how to.


Homework Equations


The sum is (integrate)3x+Sin(x^3)+1


The Attempt at a Solution


I've tried substituting u for x^3 but I don't know where to go from there considering du=3x^2.dx, which isn't relevant to my equation in any way.
 
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You are not going to find any elementary function anti-derivative for this.
 
That's what I figured. So what do I do with it?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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