Question

${\int }^{}x{\sec }^{2}xdx$

Answer 1

Now,

${\int }^{}x{\sec }^{2}xdx$

$=x.{\int }^{}{\sec }^{2}xdx$$-\int 1.\left({\int }^{}{\sec }^{2}xdx\right)dx$ [ Using method of by parts]

$=x\tan x-\log |\sec x|+c$ [ Where $c$ is integrating constant]