$\int \frac{\sec ^2 x}{(\sec x+\tan x)^{5 / 2}} d x=$

• A

  $-\frac{(\sec x+\tan x)^{5 / 2}}{5}-\frac{(\sec x+\tan x)^{7 / 2}}{7}+c$
• B

  $-\frac{(\sec x-\tan x)^{5 / 2}}{5}-\frac{(\sec x-\tan x)^{7 / 2}}{7}+c$
• C

  $-\frac{(\sec x+\tan x)^{3 / 2}}{3}-\frac{(\sec x+\tan x)^{7 / 2}}{7}+c$
• Correct answer
  D

  $-\frac{(\sec x-\tan x)^{3 / 2}}{3}-\frac{(\sec x-\tan x)^{7 / 2}}{7}+c$

Hence, the correct answer is option: 'D'.