Integration of (cosx/ (2-cosx))

[Mo]

Homework Statement

integrate with respect to x

Homework Equations

integral of cos x / (2 - cos x) dx

The Attempt at a Solution

I attempted to use the substitution of tan (x/2) but got lost in it. I don't think it was correct to subsititute t = tan(x/2) because it was not in the correct form. [am i right in thinking to substitute in t=tan(x/2) we need an equation of the form 1 / (a + bsinx + ccosx) ?]

I also tried dividing top and bottom by cos x but I am unsure if this would lead me anywhere.

I'm hoping for a little pointer in how to start.

Thanks.

 

[siddharth]

The Attempt at a Solution

I attempted to use the substitution of tan (x/2) but got lost in it. I don't think it was correct to subsititute t = tan(x/2) because it was not in the correct form. [am i right in thinking to substitute in t=tan(x/2) we need an equation of the form 1 / (a + bsinx + ccosx) ?]

(i) The substitution of tan(x/2) is sometimes used when the integrand is a rational function of sin and cos. You might find http://www-math.mit.edu/~djk/18_01/contents.html" link useful.

(ii) In your problem, try eliminating the cos function from the numerator first. Here's a hint, try adding and subtracting '2' (to the negative of the integrand) in the numerator. Can you take it from here?

 

[Mo]

try adding and subtracting '2' (to the negative of the integrand) in the numerator.

Thank you very much indeed! I do not think I would have got that in a loooong time! Thanks for the link as well.

Regards,
Mo.