Improper Integral 1/(x√(1+x²)) via Substitution to an Inverse Hyperbolic

Integrals of the form 1/(x·√(x²±a²)) are antidifferentiated by the reciprocal substitution x = 1/t, which collapses them to ±1/√(1±t²) — an inverse-hyperbolic (or arcsin) form. The improper version converges because the tail decays like 1/x².