# Is it true ?

1. Mar 11, 2006

### roger

Is the integral (in the interval x=0, x=1) of 1/ (x^x) dx = 1+(1/(2^2)) + (1/ 3^3))+(1/(4^4) ).... ?

If it is, how would one go about proving it...?

2. Mar 11, 2006

### DeadWolfe

It is true.

The jist of the proof isto start by rewriting 1/(x^x) in terms of exponentionals, then rewriting that using the McLuarin series for e^x, then integrating term by term using parts.

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