Has anybody seen an integral of the following form or has some intuition on solving the following integral
$$\int\limits_{ - \infty }^{q} {{t_\nu }\left( x \right)\log \left( {\frac{{{x^2}}}{\nu } + 1} \right)} dx $$ where $${t_\nu }\left( x \right) = \frac{{\Gamma \left( {\frac{{\nu + 1}}{2}} \right)}}{{\sqrt {\pi \nu } \cdot \Gamma \left( {\frac{\nu }{2}} \right)}}{\left( {1 + \frac{{{x^2}}}{\nu }} \right)^{ - \frac{{\left( {1 + \nu } \right)}}{2}}}$$
I tried a bunch of substitutions along with integration by parts but none seem to simplify the integral. I tried mathematica too, but it failed. I can evaluate it numerically but was wondering if I missed something obvious