Question

Integrate cosx/(sinx-1)

Answer 1

Look carefully. Making an appropriate substitution will greatly simplify this integration.

Answer 2

Would you split it apart and use trig identities?

Answer 3

Or is that over complicating it

Answer 4

I don't readily see any way to "split it apart." I think your best bet is substitution. Again, I ask you to consider what might be an appropriate substitution here.

Answer 5

U=sinx I suppose

Answer 6

\[\int\limits_{}^{}\frac{ \cos x dx }{\sin x - 1 }\]

Answer 7

isn't there a standard integral for f'(x)/ f(x) if my memory serves me right?

Answer 8

I'd encourage you to try that and then judge for yourself whether or not u=sin x is an appropriate substitution.

Answer 9

Yes, @cwrw238, there is! But let's help @howdoik finish this problem using a substitution that may lead to using your suggestion. Thanks.

Answer 10

Alright, one sec

Answer 11

oh ok
fair enough

Answer 12

@howdoik: The question I'm posing for you is this: Which is the better substitution, u=sin x or u=sin x - 1, and why?

Answer 13

Omg, I'm an idiot. Sinx-1 for u sub, then you get -du/u, hence -ln|sinx-1|+C...

Answer 14

If u = sin x, du = ?
If u = sin x - 1, du = ?

Answer 15

Looks good...but can you convince me that you need that (-) sign?

Answer 16

I over complicated it and got it wrong on my test haha. Crap.

Answer 17

I'm sorry. I admire you for pursuing this to make sure you know how to solve it even after your test!

Answer 18

Yeah, these questions really bother me and I like to check after the quiz's if I did it right or not I'm just always curious. Thanks again mathmale, and there's not suppose to be a negative sign. Derivative of sinx = cosx not -cosx, sorry.