Can You Tackle This Improper Integral Challenge?

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Your limit is wrong. xln x- x goes to 0 as x goes to 0, not infinity. Rewrite it as xlnx- x= x(ln x- 1)= (ln x-1)/(1/x) and use L'Hopital's rule.
 
thanks
 
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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