If you are doing integrals right now, you have to have come across the derivative of tanx from differential calc class. No offense, but its the most basic derivative and identity is so common, I just thought you already should have known. I've seen you help many people on this board with integrals, I assumed that you would already knew or maybe you just had a brain fart or something. Its alright I have moments like these also.
In fact, I just look through your attachment right there. You didn't even need Mathgicians or my suggestions for that identity, you got it yourself! 1/cos^2 x is sec^2 x :D You just needed to notice that was the derivative of tan x, instead of using cos^2 x = (1+cos 2x)/2