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[ + inf
E(v) = | tanh(arctanh(M)v) * e^[-(v-1)^2/(2S^2)]/(sqrt(2*pi)S) dv
I didn't bother finding the antiderivative -- wolfram alpha couldn't figure anything out even with extended computation time and it doesn't look feasible.
Now i have the expression Q/R (where Q is constant) that i want to plug into E. However, if i replace all the v with Q/R, i'm left with dv. No numerical integrators i've found will take a function as the thingy behind d and i don't even know if it makes sense to do so, so i'm forced to solve it somehow.
i tried change of variables:
u = Q/R, du/dv = 1 because du = dv. Not helpful.
According to wolfram alpha the integral of f(g(x)) is indeterminite, so that doesn't help.
So how can i plug an expression into a integral?