# Smart Fish

Calculus Level 4

Let $$\displaystyle f(x) = \frac 1{1+e^{1/x}}$$. If

$PV\ \int_{-1}^{1} \frac{d}{dx} f(x) \ dx = \lambda + \frac{1-e}{1+e},$

where $$\lambda$$ is some constant, what is the value of $$\lambda$$?

Note: The "$$PV$$" before the integral indicates the Cauchy principal value.

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