Parameter Integration of Bubble Integral

[Elmo]

TL;DR Summary

Cant figure out how this PV bubble integral has been solved.

Referring to this link : https://qcdloop.fnal.gov/bubg.pdf
Using Mathematica Integrate command to solve it does not give the result stated here but I am unclear as to how they got to the result in the 4th line.
It is clear that the integrand (1st line) can diverge for certain values of the Feynman parameter λ and this is presumably why they find the roots of the expression in the denominator. I just dont know what they did to solve this loop integral and express the result in terms of the roots.

 

[vanhees71]

Maybe they used some deformation of a complex contour for the $\lambda$ integral integrating somehow around the branch cut of the ln?

 

[Couchyam]

Just factor the quadratic argument of the logarithm as $(\lambda-\lambda_1)(\lambda - \lambda_2)$, expand the logarithm into $\log(\lambda - \lambda_1)+\log(\lambda - \lambda_2)$ (modulo constant prefactors) and integrate by parts.