Solving the Logarithmic Integral of Ln(y-1)/y^2 by Hand

[wilysrevenge]

I have been working on a solid state physics homework problem, and I have gotten the answer down to an integral that I am unsure how to do by hand. I can plug it into Mathematica, and I receive the correct answer (I am asked to show something) but I would like to know how to do this integral by hand.

Integral of Ln(y-1) / y^2

 

[Dick]

It's an easy integration by parts. Let u=ln(y-1) and v=(-1/y). Your integral is u*dv. Is that enough of a hint? If not then for the second integral v*du use partial fractions.

 

[wilysrevenge]

Ahh... I tried the integration by parts approach, but wasn't sure where to go from there. I hadn't done partial fractions in a long while and did not notice I could separate it that easily. Thank you.