JEE MAIN - Mathematics Hindi (2019 - 9th January Morning Slot - No. 17)
$$x^{2} \neq \mathrm{n} \pi+1, \mathrm{n} \in \mathrm{N}$$ (प्राकृत संख्याओं का समुच्चय), के लिए समाकलन $$\int x \sqrt{\frac{2 \sin \left(x^{2}-1\right)-\sin 2\left(x^{2}-1\right)}{2 \sin \left(x^{2}-1\right)+\sin 2\left(x^{2}-1\right)}} \mathrm{d} x$$ बराबर है- (जहाँ $$\mathrm{c}$$ एक समाकलन अचर है)
$$\log _{\mathrm{e}}\left|\frac{1}{2} \sec ^{2}\left(x^{2}-1\right)\right|+\mathrm{c}$$
$$\frac{1}{2} \log _{\mathrm{e}}\left|\sec \left(x^{2}-1\right)\right|+\mathrm{c}$$
$$\frac{1}{2} \log _{\mathrm{e}}\left|\sec ^{2}\left(\frac{x^{2}-1}{2}\right)\right|+\mathrm{c}$$
$$\log _{\mathrm{e}}\left|\sec \left(\frac{x^{2}-1}{2}\right)\right|+\mathrm{c}$$
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