# A trigonometric integration

1. May 20, 2012

### msandeep92

Hi everyone,

In my research project, i am struck with an integration. Can someone help me out:

dx/(1-k*sin2x)

Thanks,
Sandeep

2. May 20, 2012

### Infinitum

Hey Sandeep.

How did you attempt this integral? It will be easier(and ethical) to help you out if you share how you worked on it.

3. May 20, 2012

### msandeep92

I tried with substitution √k*sinx = t;

But it ends up with ∫dt/[(1 - t2/k)*(1 - t2)]

I dont know how to go ahead with this.

I tried with ksin2x = t also. But that too doesnt work.

Please help me. This is one of the last parts of a huge integration i am doing...

Thanks,
Sandeep.

4. May 20, 2012

### Infinitum

Try breaking $1-ksin^{2}x$ into $(1-\sqrt{k}sin x)(1+\sqrt{k}sinx)$

Now try splitting the term into two simple integrals of the form $\frac{1}{a+bsinx}$

5. May 20, 2012

### msandeep92

But it is (1 - ksin2x).

So, how can we split it into two simple integrals?

Sandeep.

6. May 20, 2012

### Infinitum

7. May 20, 2012

### msandeep92

Thank you.

Will Go through it..

Sandeep.