Equals to (for some arbitrary constant )

MATHEMATICS · Single correct · CBSE · Mathematics · Integrals · Integrals

Problem

∫sec⁡2x(sec⁡x+tan⁡x)9/2dx\int \frac{\sec^2 x}{(\sec x + \tan x)^{9/2}} dx equals to (for some arbitrary constant KK ) (1) −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 (2) 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 (3) −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 (4) 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

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