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