Therefore, ∫ cot x dx = ln|sin x| + C.
This looks a lot like the previous example, doesn’t it?
Example 12: Find ∫sec x dx.
You could rewrite this integral as
However, if you try u-substitution at this point, it won’t work. So what should you do? You’ll probably
never guess, so we’ll show you: Multiply the sec x by . This gives you
Now you can do u-substitution. Let u = sec x + tan x du = (sec x tan x + sec^2 x) dx.
Then rewrite the integral as
∫
Pretty slick, huh?
The rest goes according to plan as you integrate.