Question: $$\int\frac{\mathrm dx}{\sqrt x \cos(1-\sqrt x)}$$
please provide a hint about the substitution. The website gives a long answer [See here.](http://www.wolframalpha.com/input/?i=int%201/%28x%5E%281/2%29cos%281-x%5E%281/2%29%29)
Wondering if there is a simplification.

Answer: 
**Hint**:

$$u = 1 - \sqrt{x} \implies du = -\frac{1}{2 \sqrt{x}} dx$$

so the integral can be written as

$$\int \frac{1}{\cos(1 - \sqrt{x})} \frac{dx}{\sqrt{x}} = \int \frac{1}{\cos{u}} \frac{du}{-2} = -\frac{1}{2} \int \sec{u} du$$
HINT: Let $u=1-\sqrt{x}$, and get the trig function out of the denominator.