CUET Mathematics 2022 23 Aug Shift 1 PYQs

If $I = \int \frac{x}{x - \sqrt{x^2 - 4}} dx = \alpha x^3 + \beta(x^2 - 4)^{\frac{3}{2}} + \gamma$, where $\gamma$ is constant of integration, then

$\int e^{(x \log 5)}e^x dx$, is:

Where $C$ is the constant of integration.

For $x \in \left(0, \frac{\pi}{2}\right)$, $\int \frac{1}{\sin^2 x + \sin 2x} dx$ is equal to