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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Let x2≠nπ−1,n∈Nx^2 \neq n \pi-1, n \in N. Then, the value of ∫x2sin⁡(x2+1)−sin⁡2(x2+1)2sin⁡(x2+1)+sin⁡2(x2+1)dx\int x \sqrt{\frac{2 \sin \left(x^2+1\right)-\sin 2\left(x^2+1\right)}{2 \sin \left(x^2+1\right)+\sin 2\left(x^2+1\right)}} d x is equal to
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Correct option: B
log⁡∣sec⁡(x2+12)∣+C\log \left|\sec \left(\frac{x^2+1}{2}\right)\right|+C
Option B is correct because after simplifying the expression inside the square root and using a trigonometric identity, the integral can be evaluated as log⁡∣sec⁡(x2+12)∣+C\log \left|\sec \left(\frac{x^2+1}{2}\right)\right|+C.

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