tan(t) = x
sec(t)^2 dt = dx
tan(t)^2 * sec(t)^2 dt/(1+tan(t)^2)^2
tan(t)^2 * sec(t)^2 dt/(sec(t)^2)^2
tan(t)^2 dt /sec(t)^2
sin(t)^2 dt
Integrate this using trigo identities on wikipedia.
tan(t) = x
sec(t)^2 dt = dx
tan(t)^2 * sec(t)^2 dt/(1+tan(t)^2)^2
tan(t)^2 * sec(t)^2 dt/(sec(t)^2)^2
tan(t)^2 dt /sec(t)^2
sin(t)^2 dt
Integrate this using trigo identities on wikipedia.