Digamma Integral Representation

Hi,

I'm trying to figure out how the integral representation of the Digamma function works.

I understand that the Digamma function is the logarithmic derivative of the Gamma function. Therefore

Since

then I would think

Anyway, the integral expression for the Digamma function is given by

How would I derive this formula?

Should I instead look at another representation of the Gamma function and work with that?

Thank you.

You have done a great job !

Your substitution is perfect (Clapping) !

so

Also

We need to make a further substitution ,

Therefore ,

!!

Or