# Lebesgue integral

1. Nov 22, 2012

### hedipaldi

1. The problem statement, all variables and given/known data
use the Lebesgue monotone convergence theorem to prove the following equality (attached)

2. Relevant equations
Lebesgue monotone convergence theorem

3. The attempt at a solution
i tried to identify a suitable monotonic sequence,from power series.

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2. Nov 22, 2012

### Ray Vickson

The integral is not clear (poor quality image). Is it
$$\int_0^1 \frac{x^p}{x-1} \log (x) dx?$$ Do you mean dm(x) = dx?

RGV

3. Nov 22, 2012

### hedipaldi

yes,this is correct.
I already solved .Thank's a lot.