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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1
The integral ∫sec⁡2x(sec⁡x+tan⁡x)9/2dx\int \frac{\sec ^2 x}{(\sec x+\tan x)^{9 / 2}} d x equals (for some arbitrary constant KK)
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Correct option: C
−1(sec⁡x+tan⁡x)11/2{111+17(sec⁡x+tan⁡x)2}+K-\frac{1}{(\sec x+\tan x)^{11 / 2}}\left\{\frac{1}{11}+\frac{1}{7}(\sec x+\tan x)^2\right\}+K
Option C (−1(sec⁡x+tan⁡x)11/2{111+17(sec⁡x+tan⁡x)2}+K-\frac{1}{(\sec x+\tan x)^{11 / 2}}\{\frac{1}{11}+\frac{1}{7}(\sec x+\tan x)^2\}+K) is correct because substituting t=sec⁡x+tan⁡xt = \sec x + \tan x and simplifying leads to the given result.

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