Can anyone tell me the following indefinite integral (antiderivative):
$$ \int \frac{a}{2} \left( 1 + \textrm{erf}(x) \right) \log\left( \frac{a}{2}\left(1 + \textrm{erf}(x) \right) \right) dx $$ $$ = \int \frac{a}{2} \textrm{erfc}(-x) \log\left( \frac{a}{2} \textrm{erfc}(-x) \right) dx $$ $$ =\ ? $$
This is the entropy of the complementary error function $ \textrm{erfc}(x) $ with negative argument. $ a $ is some parameter, i.e. a constant. $ \log(x) $ is the natural logarithm.
This integral seems to be very tricky. Thank you in advance.