Integration by substitution problem

madmike159
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Homework Statement



Using a suitable substitution find the solution to:

∫ (x+2)50(x+1)dx


Homework Equations





The Attempt at a Solution



I can't find a solution to this using substitution. Wolfram alpha give an answer that is too long to be calculated by hand. Can anyone work out the solution, or is there a mistake in the question which means it can't be solved?
 
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Let\; u=x+2
 
What do you get if you let u= x+ 2? That seems to me to be the obvious substitution. It is certainly not "too long to be calculated by hand".
 
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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