CUET Mathematics 2025 14 May Shift 2 PYQs

If $\int \frac{1-x}{\sqrt{1+x}} dx = a\sqrt{1-x^2} + b \sin^{-1}x + C$, Where C is an arbitrary constant, then which of the following are TRUE?

(A) $\alpha = 1$

(B) $\alpha = -1$

(C) $\beta = 1$

(D) $\beta = -1$

Choose the correct answer from the options given below:

The value of the definite integral $I = \int_{1}^{2} \frac{1}{x(1 + x^2)}dx$ is:

For $x \in \mathbb{R} - \{-1,0,1\}$, $\int \frac{1}{x - x^5}dx$ is equal to