CUET Mathematics 2025 21 May Shift 2 PYQs

$\int \frac{x}{(x-1)(x-2)} dx$ is equal to ( where $C$ is a constant of integration)

If the integral $I = \int \frac{x^2}{\sqrt{1+x}} dx = \frac{2}{3}(1+x)^{3/2} - \frac{8x}{15}(1+x)^{3/2} + \frac{2(1+x)^{5/2}}{15} + C$; C is constant of integration, then the value of a is:

The value of $\int_{0}^{\pi/2} \frac{ an^2 x}{\cot^2 x + an^2 x} dx$ is