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MathsJEE Main 5 Apr 2026, Shift 2·Q18·MCQ·Moderate

Definite Integration · Definite integral by substitution

Let (21−a+21+a)\left(2^{1-a} + 2^{1+a}\right), f(a)f(a), (3a+3−a)\left(3^{a} + 3^{-a}\right) be a A.P. and α\alpha be the minimum value of f(a)f(a). Then the value of the integral ∫log⁡e(α−1)log⁡e(α)dx(e2x−e−2x)\int_{\log_e(\alpha-1)}^{\log_e(\alpha)} \frac{dx}{\left(e^{2x} - e^{-2x}\right)} is:
  1. (1)12log⁡e(43)\dfrac12\log_e\left(\dfrac43\right)
  2. (2)14log⁡e(43)\dfrac14\log_e\left(\dfrac43\right)
  3. (3)12log⁡e(85)\dfrac12\log_e\left(\dfrac85\right)
  4. (4)14log⁡e(85)\dfrac14\log_e\left(\dfrac85\right)

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