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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy
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Application +4 | -1
∫sec⁡2x(sec⁡x+tan⁡x)9/2dx\int \frac{\sec ^2 x}{(\sec x+\tan x)^{9 / 2}} d x equals to (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 (\frac{{-1}}{{(\sec x+\tan x)^{{11 / 2}}}}\left{\frac{{1}}{{11}}+\frac{{1}}{{7}}(\sec x+\tan x)^2\right\}+K\frac{{-1}}{{(\sec x+\tan x)^{{11 / 2}}}}\left{\frac{{1}}{{11}}+\frac{{1}}{{7}}(\sec x+\tan x)^2\right\}+K) is correct because it represents the result of the given integral after applying substitution and simplification.

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