Smart Fish

Calculus Level 4

Let f(x)=11+e1/x\displaystyle f(x) = \frac 1{1+e^{1/x}}. If

PV 11ddxf(x) dx=λ+1e1+e,PV\ \int_{-1}^{1} \frac{d}{dx} f(x) \ dx = \lambda + \frac{1-e}{1+e},

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

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

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