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Problem ∫ sec 2 x ( sec x + tan x ) 9 / 2 d x \int \frac{\sec^2 x}{(\sec x + \tan x)^{9/2}} dx ∫ ( s e c x + t a n x ) 9/2 s e c 2 x d x equals to (for some arbitrary constant K K K )
a. − 1 ( sec x + tan x ) 11 / 2 { 1 11 − 1 7 ( 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 ( s e c x + t a n x ) 11/2 − 1 { 11 1 − 7 1 ( sec x + tan x ) 2 } + K
b. 1 ( sec x + tan x ) 11 / 2 { 1 11 − 1 7 ( 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 ( s e c x + t a n x ) 11/2 1 { 11 1 − 7 1 ( sec x + tan x ) 2 } + K
c. − 1 ( sec x + tan x ) 11 / 2 { 1 11 + 1 7 ( 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 ( s e c x + t a n x ) 11/2 − 1 { 11 1 + 7 1 ( sec x + tan x ) 2 } + K
d. 1 ( sec x + tan x ) 11 / 2 { 1 11 + 1 7 ( 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 ( s e c x + t a n x ) 11/2 1 { 11 1 + 7 1 ( sec x + tan x ) 2 } + K
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