Greetings mates,

If anyone can help me solve the following integral using the change of variable ჯ = cosმ

The ^ means to the power, so 2Cos^2მ is 2 multiplied by the squared of Cosმ ( just to avoid confusion ).

The given integral is:

I = ∫[(1+ჯ)/(1-ჯ)]^½dჯ

I already worked it out using other methods like taking t^2 = (1+ჯ)/(1-ჯ) and then solving in terms of t. I found out the solution. However, the method of change of variable using Cosმ is not working. For starters,

I = ∫[(1+cosმ)/(1-cosმ)]^½dcosმ = - ∫[(2Cos^2B)/(2Sin^2B)]^½ sinმdმ where B = მ/2

This implies, I = - ∫[1/|Tan^2B|] sinმdმ

--> I = - ∫ (sinმdმ / Tan^2B )

How to cotinue from here? I've tried many methods using integrations by parts, by nothing worked out.

Thanks in advance.