Question

need a hint, integrate sec^2(cosx) dx

Answer 1

I think chain rule?

Answer 2

hm, how would I start it?

Answer 3

F'(x) = f'(g(x)) g'(x).

Answer 4

what is the derivative of sec^2(x) ?

Answer 5

2tan(x)sec^2(x)? but I'm trying to integrate

Answer 6

Opps my bad..sorry

Answer 7

it's ok, any idea how to integrate this?

Answer 8

Change sec^2 to 1-tan^2 then convert equation to sin /cosine.
sec^2(cosx) = 1 - tan^2(cosx)
=[1-sin^2(cosx)/cos^2(cosx)]. . . . . . . . . . .

Answer 9

then
Take t=cosx
So dt=-sinxdx
Thus, (1) becomes
1 - sin^2(t)/cos^2(t)-dt/sinx

Answer 10

alright, ty