How do i get to solve this integral,i have no idea whatsoever so no

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The integral presented involves a complex expression of the form [x^(1/x)] raised to itself multiple times, which is confusing to the poster. The poster expresses frustration and a lack of understanding regarding how to approach solving this integral. Several users suggest breaking down the expression and exploring its properties to simplify the problem. Others recommend looking into related mathematical concepts or techniques that could aid in solving such integrals. Overall, the discussion highlights the challenges of tackling intricate mathematical expressions without a clear strategy.
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how do i get to solve this integral,i have no idea whatsoever so no one should expect what i have done.it was presented to me by a colleague
[x^(1/x)]^[x^(1/x)]^[x^(1/x)]^[x^(1/x)]^[x^(1/x)]^[x^(1/x)]^[x^(1/x)]...
 
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that is ridiculas it makes no sense at all
 
I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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