Question

Write the value of $\int \sec xdx$

Answer 1

$\int \sec xdx$

Dividing numerator & denominator by $(\sec x+\tan x)$

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

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

Let $u=\sec x+\tan x$

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

$=\int \frac{1}{u}du$

$=\ln \mid u\mid$

$=\ln \mid \sec x+\tan x\mid$