Integral of (5x+7)^28: Step-by-Step Solution

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Homework Statement


S=integral symbol
S(5x+7)^28


Homework Equations


Substitution


The Attempt at a Solution


let u = 5x+7
du = 5
S u^28 du
= (u^29)/29 du
= [5(5x+7)^29]/29

is this correct? I'm not sure...
 
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Where did the extra 5 come from?
 
nevermind i figured it out the answer is [(5x+7)^29]/145. stupid mistakes
 
Yea, that looks right.
 
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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