What is the solution to this slight integral problem?

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Homework Statement



∫ \frac{5e^{\frac{1}{y}}}{3y^{2}}

Homework Equations



u=5e^{\frac{1}{y}}

u'= -5e^{\frac{1}{y}}


The Attempt at a Solution



I keep getting: -\frac{5e^{\frac{1}{y}}}{3y^{2}} +c but I know that there shouldn't be a y^{2} in the denominator.

 
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Disregard this post; I've discovered my mistake.
 
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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