Question

What is the indefinite integral of secx

Answer 1

write as \[\frac{\sec(x)}{1}\]

and multiply the top and bottom by

\[\sec(x)+\tan(x)\]

Answer 2

then set
u = sec +tan
du = sectan + sec^2

Answer 3

I got it but how do i know I'm supposed to multiply top/bottom by secx + tanx?

Answer 4

great question, its just one of those integrals where you have to find a way to manipulate it to make the substitution work.
the reason we use sec +tan is because we know its derivative will cancel the numerator

Answer 5

thanks again!