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1995

JEE Main 1995 Mathematics question on Indefinite Integration

The value of ∫cos⁡3x+cos⁡5xsin⁡2x+sin⁡4xdx\int \dfrac{\cos^3 x + \cos^5 x}{\sin^2 x + \sin^4 x} dx is
  1. A.
    sin⁡x−6tan⁡−1(sin⁡x)+c\sin x - 6\tan^{-1}(\sin x) + c
  2. B.
    sin⁡x−2(sin⁡x)−1+c\sin x - 2(\sin x)^{-1} + c
  3. C.
    sin⁡x−2(sin⁡x)−1−6tan⁡−1(sin⁡x)+c\sin x - 2(\sin x)^{-1} - 6\tan^{-1}(\sin x) + c
  4. D.
    sin⁡x−2(sin⁡x)−1+5tan⁡−1(sin⁡x)+c\sin x - 2(\sin x)^{-1} + 5\tan^{-1}(\sin x) + c
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Correct option: C

[1995]

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