I have a problem with this integral
$$\int_\ \frac{\cos x }{\sin x \sqrt{1+\cos^2x}} \, dx$$
Using substitution $u = \sin x $ we get
$$\int_\ \frac{1 }{\ u \sqrt{2-u^2}} \, du$$
I think the next step is to use simple fractions, but I don't know how to do it.