What is the Antiderivative of a Complex Square Root Function?

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Homework Statement



Antiderivative of sqrt[e^x+ln(x^2)+1]

Homework Equations





The Attempt at a Solution



(2[(e^x+ln(x^2)+1)^(3/2)]x^2)/[3(e^x+2x)]
 
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No, that is incorrect and I don't think this can by integrated in terms of elementary functions. What you have done, integrating u^{1/2} as (3/2)u^{3/2} and then dividing by the derivative of u, can only be done if u is linear so that u' is a constant. Constants can be "moved" inside and outside of an integral. functions of the variable of integration cannot.
 

Thread 'Finding the nth roots of a complex number'

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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