What is the integration of tanx?

The integral of tan(x) dx = ln | sec(x) | + c

to solve... tan(x) = sin(x)/cos(x)

the integral of (sin(x)/cos(x) dx) ... let u = cos(x) then du = -sin(x) dx

= the integral of (1/u -du)

= -ln | u | + c

= -ln | cos(x) | + c

= ln | (cos(x))^-1 | + c ... or ... ln | 1/cos(x) | + c

= ln | sec(x) | + c