# Integrating 1/sin*|sin|

1. Feb 7, 2010

### NanakiXIII

1. The problem statement, all variables and given/known data

I need to solve the integral

$$\int \frac{dx}{\sin{x} |\sin{x}|}.$$

2. Relevant equations

-

3. The attempt at a solution

I know it's possible, the solution is $$-\frac{\cos{x} |\sin{x}|}{\sin^2{x}}$$, and I probably need to write the absolute as the square root of a square. I also probably need a substitution to simplify. I'm not having any luck finding such a substitution, however.

2. Feb 7, 2010

### ideasrule

Integrate it for sinx>0, then for sinx<0. Compare.

3. Feb 8, 2010

### NanakiXIII

That worked perfectly. Thanks. I suppose that's the usual way to tackle an integral over an absolute value?