Does anybody know a relatively intuitive method to integrate 1/cos(x) ? Thanks!

Question

diyadiya · Answer

$$\int\limits secxdx= \log|secx+tanx|+C$$

diyadiya · Answer

@Mimi_x3 You were right =)

mimi_x3 · Answer

Write it as:
$$\int\limits secxdx  $$
Then..
$$\int\limits\frac{secx*secx+tanx}{1*secx+tanx}  $$
I was wrong diya, lol.

mimi_x3 · Answer

lol, sorry.
$$\large \int\limits\frac{\sec^{2}x+secxtanx}{secx+tanx}  $$
happy now? :P

anonymous · Answer

Thanks, all of you :) Mimi's way is quite nice, but is there no way that doesn't involve memorising a "trick" like that one?

diyadiya · Answer

$$\int\limits\limits\frac{sec^2x+secxtanx}{secx+tanx}$$
Let Secx+tanx =u
$$du/dx=secxtanx+\sec^2x$$
$$\int\limits \frac{du}{u}=\log|u|+C=\log|secx+tanx|+C$$

anonymous · Answer

See http://www.math.com/tables/integrals/more/csc.htm

amistre64 · Answer

the integration for sec(x) was discovered prior to the calculus being formed.

amistre64 · Answer

Mercator and mapmaking are involved.