Integrate S x^2(e^((x^3)+1)) with Parts - Step-by-Step

satxer
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S x^2(e^((x^3)+1))

I know I have to use integration by parts, and I'm guessing I should find the derivative of e^((x^3)+1), but I really have no idea where to start...
 
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You don't have to do an integration by parts. It's a simple u substitution. You should always try that first.
 
do you have to use parts? how about just a substitution?
 
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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