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MathsJEE Main 5 Apr 2026, Shift 1·Q18·MCQ·Moderate

Definite Integration · Definite integral by substitution

The value of the integral ∫0∞log⁡e(x)x2+4 dx\displaystyle\int_0^{\infty}\frac{\log_e(x)}{x^2 + 4}\,dx is:
  1. (1)πlog⁡e(2)2\dfrac{\pi\log_e(2)}{2}
  2. (2)πlog⁡e(2)4\dfrac{\pi\log_e(2)}{4}
  3. (3)1+πlog⁡e(2)1 + \pi\log_e(2)
  4. (4)2+πlog⁡e(2)2 + \pi\log_e(2)

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