Partial Fractions Help: Integrating √(1+x^2)/x for Homework

Moenga
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Homework Statement


∫▒√(1+x^2 )/x dx


Homework Equations





The Attempt at a Solution


I don't know how to break this up. I know we break partial fraction problems up based on their denominator, however the denominator i this problem is just 'x'.
 
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Moenga said:

Homework Statement


∫▒√(1+x^2 )/x dx


Homework Equations





The Attempt at a Solution


I don't know how to break this up. I know we break partial fraction problems up based on their denominator, however the denominator i this problem is just 'x'.

Just write it as the sum of two fractions. No partial fractions needed.
 
I know its simple to do it that way. The problem is asking to use partial fractions
 
That problem is not appropriate to partial fractions. The method makes no sense for it.
 
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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