integration 101

[freudian_slip]

ok, so i have a fairly simple integration by parts problem here but i am missing something.

it is integrate sec^2xtanxdx

i set it to be secx(secxtanx) and then i made u=secx du=secxtanxdx dv=secx(secxtanx)dx

so, then i got

integrate(secx(secxtanx)dx) = secxsecx - integrate(secx(secxtanx)dx)

and i am back where i started. what i am missing?