How do I solve this integration problem?

Question

The question is- Find $\int\frac{\sec^xx}{\sqrt{\tan x}}dx$

What I've tried: $$\int\frac{\sec^{x-2}x\sec^2x}{\sqrt{\tan x}}dx$$

Let $\tan x = t$.

$$\int\frac{\sec^{x-2}x}{\sqrt{t\,}}dt$$

What should I do next? Any sort of help is appreciated.

Answer 1

You can't. Integrands of the form $f^x(x)$ usually have no closed-form antiderivative, by the Liouville theorem.

The probability that your problem statement is wrong equals $1-\epsilon$.

And IMO the probability that the true question is

$$\int\frac{\sec^2x}{\sqrt{\tan x}}dx$$

equals $1+\epsilon$.