Let \(\left(2^{1-\mathrm{a}} + 2^{1+\mathrm{a}}\right), f(a),\left(3^{\mathrm{a}}+3^{-\mathrm{a}}\right)\) be in A.P. an…

Let \(\left(2^{1-\mathrm{a}} + 2^{1+\mathrm{a}}\right), f(a),\left(3^{\mathrm{a}}+3^{-\mathrm{a}}\right)\) be in A.P. and \(\alpha\) be the minimum value of \(f (a)\). Then the value of the integral \(\int_{\log _e(\alpha-1)}^{\log _e(\alpha)} \frac{d x}{\left(e^{2 x}-e^{-2 x}\right)}\) is:

[JEE Main 2026, 5 Apr (Shift 2)]