Question

$\int \frac{\sec x}{\sqrt{\log(\sec x + \tan x)}} dx =$

Answer 1

$2\sqrt{\log(\sec x + \tan x)} + C$

Answer 2

1. Substitute $u = \log(\sec x + \tan x)$.

2. Calculate the differential $du = \frac{d}{dx}(\log(\sec x + \tan x)) dx = \sec x dx$.

3. Rewrite the integral in terms of $u$: $\int \frac{1}{\sqrt{u}} du$.

4. Evaluate the integral: $\int u^{-1/2} du = 2u^{1/2} + C$.

5. Substitute back $u = \log(\sec x + \tan x)$ to obtain the final result $2\sqrt{\log(\sec x + \tan x)} + C$.