Quick integrating question (part of a series question)

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Quick integrating question...(part of a series question)

Still studying for my exam...


Came across this example and I don't know what the method is for integrating this type of problem? (I'm using it to do the integral test for series). How did they get rid of the x^3? thanks for the help :-)

int.jpg
 
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Well what's the derivative of -1/3 * exp(-x^3)?
 
Or: let u= x2 so that du= 3x2 dx.
 
ahhh...i see it now. 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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