Closed form for the definite integral $\int_3^5\exp\left[\frac{-3.91}{V}\left(\frac{\lambda}{0.55}\right)^{-q}R\right]\,\mathrm d\lambda$

Question

I am stuck on the following definite integral: $$\tau=\int_3^5\exp\left[\frac{-3.91}{V}\left(\frac{\lambda}{0.55}\right)^{-q}R\right]\,\mathrm d\lambda$$ Is it possible to solve it in a closed form ? Thanks.

Answer 1

Since the limits of the integration are pretty "exotic" (not $0,1$ or $\infty$), I would only expect the closed form if the indefinite integral has it. For the latter, WA gives relatively closed solution which may be of interest to you - just follow the link.