Question

The integraldx equals (for some arbitrary constant k)

• A. $\frac{-1}{(\sec x+\tan x{)}^{\frac{11}{2}}}\{\frac{1}{11}-\frac{1}{7}(\sec x+\tan x{)}^2\}+k$
  
• B. $\frac{1}{(\sec x+\tan x{)}^{\frac{11}{2}}}\{\frac{1}{11}-\frac{1}{7}(\sec x+\tan x{)}^2\}+k$
  
• C. $\frac{-1}{(\sec x+\tan x{)}^{\frac{11}{2}}}\{\frac{1}{11}+\frac{1}{7}(\sec x+\tan x{)}^2\}+k$
  
• D. $\frac{1}{(\sec x+\tan x{)}^{\frac{11}{2}}}\{\frac{1}{11}+\frac{1}{7}(\sec x+\tan x{)}^2\}+k$
  

Answer 1

The correct option is C $\frac{-1}{(\sec x+\tan x{)}^{\frac{11}{2}}}\{\frac{1}{11}+\frac{1}{7}(\sec x+\tan x{)}^2\}+k$

Put sec x + tan x = t

(sec x tan x + sec²x) dx = dt

sec x. t dx = dt