Computing the integral $ \int_0^{\infty} e^{-\phi^2+\phi}\cdot \phi^{2} \ln(1-2x\cos\phi+x^2)\, d\phi. $

Question

Integrate $$ \int_0^{\infty} e^{-\phi^2+\phi}\cdot \phi^{2} \ln(1-2x\cos\phi+x^2) \, d\phi. $$ Something that may help $(1-2x\cos\phi+x^2)=(1-xe^{i\phi})(1-xe^{-i\phi})$. And using the series expansion $$ \ln(1-z)=-\sum_{n=1}^\infty \frac{z^n}{n} $$ where $|z=xe^{\pm i\phi}| \leq 1$. The series is absolutely and uniformly convergent. Any method is okay.