Question

$\int (\sec x+\tan x{)}^{2}dx=$

• A. $2(\sec x+\tan x)-x+c$
• B. $1/3(\sec x+\tan x{)}^3+c$
• C. $\sec x(\sec x+\tan x)+c$
• D. $2(\sec x+\tan x)+c$

Answer 1

Answer: (A)

$\int (\sec x+\tan x{)}^{2}dx=\int \left({\sec }^{2}x+{\tan }^{2}x+2\sec x\tan x\right)dx$
$=\int \left(2{\sec }^{2}x-1+2\sec x\tan x\right)dx$
$=2(\sec x+\tan x)-x+c$