Question

Integrate the following function: $\int \sec x(\sec x+\tan x)dx$

• A. $\tan x+\frac{1}{\cos x}+c$
• B. $\cot x+\frac{1}{\sin x}+c$
• C. $\tan x-\frac{1}{\cos x}+c$
• D. $\cot x-\frac{1}{\cos x}+c$

Answer 1

The correct option is A $\tan x+\frac{1}{\cos x}+c$

$I=\int secx(secx+tanx)dx$

$I=\int (se{c}^{2}x+secx.tanx)dx$

$I=\int se{c}^{2}xdx+secx.tanxdx$

$I=tanx+secx+C$

$I=tanx+\frac{1}{cosx}+C$

Correct option is $A$