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JEE Main 2019 · 9 Jan · Shift I

JEE Main 2019 Mathematics question on Indefinite Integration

For x2≠nπ+1x^2 \neq n\pi + 1, n∈Nn \in N (the set of natural numbers), the integral
∫x2sin⁡(x2−1)−sin⁡2(x2−1)2sin⁡(x2−1)+sin⁡2(x2−1) dx\int x\sqrt{\frac{2\sin(x^2-1)-\sin 2(x^2-1)}{2\sin(x^2-1)+\sin 2(x^2-1)}}\,dx
is equal to (where CC is a constant of integration)
  1. A.
    12log⁡e∣sec⁡(x2−1)∣+C\frac{1}{2}\log_e|\sec(x^2-1)|+C
  2. B.
    log⁡e∣sec⁡(x2−12)∣+C\log_e\left|\sec\left(\frac{x^2-1}{2}\right)\right|+C
  3. C.
    log⁡e∣12sec⁡2(x2−1)∣+C\log_e\left|\frac{1}{2}\sec^2(x^2-1)\right|+C
  4. D.
    12log⁡e∣sec⁡2(x2−12)∣+C\frac{1}{2}\log_e\left|\sec^2\left(\frac{x^2-1}{2}\right)\right|+C
Show answer

Correct option: B

[JEE Main 2019 · 9 Jan · Shift I]

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