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MathsJEE Main 8 Apr 2026, Shift 2·Q16·MCQ·Moderate

Definite Integration · Definite integral by substitution

The value of the integral ∫02x(x2+x+1)(x+1)(x4+x2+1) dx\int_0^2 \frac{\sqrt{x(x^2 + x + 1)}}{\left(\sqrt{x+1}\right)\left(\sqrt{x^4 + x^2 + 1}\right)}\,dx is equal to:
  1. (1)13log⁡e(3−22)\dfrac13\log_e\left(3 - 2\sqrt2\right)
  2. (2)23log⁡e(4+2)\dfrac23\log_e\left(4 + \sqrt2\right)
  3. (3)23log⁡e(3+22)\dfrac23\log_e\left(3 + 2\sqrt2\right)
  4. (4)13log⁡e(1+62)\dfrac13\log_e\left(1 + 6\sqrt2\right)

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