Question

$\int \sec x(\sec x+\tan x)dx$ is equal to (where $C$ is the constant of integration)

• A. $\tan x+\sec x+C$
• B. $\tan x-\sec x+C$
• C. $\tan x+\cos x+C$
• D. $\cot x+\sec x+C$

Answer 1

The correct option is A $\tan x+\sec x+C$

On expanding the expression,
$\int \sec x(\sec x+\tan x)dx=\int ({\sec }^{2}x+\sec x\tan x)dx$
By taking terms separately, we get
$=\int {\sec }^{2}xdx+\int \sec x\tan xdx$
$=\tan x+\sec x+C$