# Calculate/approximate the integral E(log|tanh(x/2)|)

1. Jan 4, 2012

### ait.abd

1. The problem statement, all variables and given/known data
I want to calculate/approximate the integral $E[log|tanh(x/2)|]$ where E is expected operator and x is a Normally Distributed Random Variable $N(\mu, 2\mu)$ where $2\mu$ is standard deviation. I am trying to find an approximation to this integral as a function of $\mu$. So in summary I want to find

$f(\mu) ≈ E[log|tanh(x/2)|]$

2. My Try
I know there exists Jensen's Inequality but don't know how different results will be if I take expectation operator inside the function.