SOLUTION: int x ^((x)/(ln x)) from 0 to 1 dx

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Question 1207774: int x ^((x)/(ln x)) from 0 to 1 dx
Answer by mccravyedwin(405) About Me  (Show Source):
You can put this solution on YOUR website!

int%28x%5E%28x%2Fln%28x%29%29%2Cdx%2C0%2C1%29

Looks really complicated, but watch how nicely it simplifies:



Take natural logs of both sides

ln%28u%29%22%22=%22%22ln%28matrix%282%2C1%2C%22%22%2C+x%5E%28x%2Fln%28x%29%29%29%29

ln%28u%29%22%22=%22%22expr%28x%2Fln%28x%29%29ln%28x%29

ln%28u%29%22%22=%22%22expr%28x%2Fcross%28ln%28x%29%29%29cross%28ln%28x%29%29

ln%28u%29%22%22=%22%22x

u%22%22=%22%22e%5Ex

int%28e%5Ex%2Cdx%2C0%2C1%29

%22%22=%22%22e%5E1-e%5E0%22%22=%22%22e-1

Answer: e-1

Simple, huh? :)

Edwin