How can we solve the following integral? $$\int_0^M \exp{\left(\frac{-0.5}{1+x^2}\right)}dx$$ , where M is very large. Does this integral converge to some constant?
2026-04-28 16:22:15.1777393335
Convergence of integral
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The integral does not converge, because for $x \to +\infty$ $$\exp\left(\frac{-0.5}{1+x^2}\right) > \frac1x$$ and $$\int_\epsilon^\infty\frac1x\mathrm dx$$ with $\epsilon > 0$ diverges.