Question

Calculate the indefinite integral of:
sec(x) dx

I would like a hint please.

Answer 1

Write
\[ \sec x = \frac{\sec x (\sec x + \tan x)}{\sec x + \tan x } \]

Answer 2

How did you get the above expression?

Answer 3

just multiply by\[\frac{\sec x+\tan x}{\sec x+\tan x}\]it's not an obvious move at first, but it works
just keep staring at the result and you will eventually see you can now integrate

Answer 4

This integral is not obvious. But ask yourself now: what is the derivative of sec x? And of tan x?

Answer 5

still pondering the integral QRA ?

Answer 6

I understand. Thank you.

Answer 7

I just had to make a substitution for this.