Proving Equality Using Lebesgue Monotone Convergence Theorem

[hedipaldi]

Homework Statement

use the Lebesgue monotone convergence theorem to prove the following equality (attached)

Homework Equations

Lebesgue monotone convergence theorem

The Attempt at a Solution

i tried to identify a suitable monotonic sequence,from power series.

 

[Ray Vickson]

Homework Statement

use the Lebesgue monotone convergence theorem to prove the following equality (attached)

Homework Equations

Lebesgue monotone convergence theorem

The Attempt at a Solution

i tried to identify a suitable monotonic sequence,from power series.

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

 

[hedipaldi]

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