How to obtain the expected value of the following function I am trying to figure out the process I should follow to obtain the expected value of
$$
\text{CNoEst(B)} = \frac{1}{2}E(\log(1+B(|S|^2)),
$$
where $S$ is a Gaussian random variable with zero mean and unit variance and B = 10 dB. The true value should be approximately equal o 1.15.
However, I have no clue as to the approach I should take. Also, I would love any recommendations regarding any extra material I should go through to get an understanding of these topics.

The expectation you wish to compute
$$
\frac{1}{2}E(\log(1+B(|S|^2)) = \frac{1}{2}\int_{-\infty}^{+\infty}\log(1+B(|x|^2) \frac{1}{\sqrt{2\pi}}e^{-\frac{x^2}{2}}\,\text{d}x,
$$
does not seem to be computable analytically, unless $B=0$ (in which case it would be zero).
However, it can be approximated by numerical integration using R. Below I'm showing you the code for doing this. The code actually defines CNoEst(B) as a function of B which internally performs the numerical integration using integrate.
cnoest_b <- function(b) {
  ff= function(x) 0.5*log(1+b*(x)^2) * dnorm(x,0,1)
  ffv= Vectorize(ff, "x")
  oo = integrate(ffv, lower = -6, upper = 6)
  return(oo)
}

> cnoest_b(10)
0.8683051 with absolute error < 6.3e-05

As you can see from the output above, CNoEst(10) $\approx 0.8683051$, which does not coincide with your claimed value of 1.15.
