Question

Evaluate the indefinite integral of:

1
----------
cos(x) - 1

dx

I would like a hint please, not the answer.

Answer 1

\[\int{dx\over\cos x-1}\]?
that's tricky I think...

Answer 2

yes

Answer 3

what if u miltiply it by (cosx+1)?

Answer 4

that should do it!

Answer 5

just be be clear @QRAwarrior shinigami meant multiply it by\[{1+\cos x\over1+\cos x} \]and use some trig identities
that is a sufficiently good tip

Answer 6

rationalization? am i right?

Answer 7

But then how would U-subsitution work from there on?

Answer 8

do you know half angle method?

Answer 9

How would you further go on? I get this:

1 + cosx
--------
(sinx)^2

dx

Answer 10

Yes that would be
(sinx)^2 = [1/2][1-cos(2x)]

Answer 11

But U-substitution would still not work...

Answer 12

its 1+cos/ -sin^2

Answer 13

Yes I realized.

Answer 14

But I do not see what I can do with
1 + cos/(1/2)(1 + cos(2x))

Answer 15

just... divide it dont simplify...

Answer 16

Got it.