CUET Mathematics 2025 2 June Shift 1 PYQs

If $\int \frac{dx}{(x-1)^2(x+2)^2} = a[1 - g(x)]^b + c$, where $c$ is a constant of integration, then which of the following are true?

(A) $a = \frac{1}{3}$

(B) $\beta = \frac{3}{4}$

(C) $3\alpha + 4\beta = 5$

(D) $g(x) = \frac{3}{(x+2)}$

Choose the correct answer from the options given below:

For $x > e$, $\int \frac{dx}{x - \sqrt{x}}$ is equal to

$\int_1^{\sqrt{3}} \frac{1}{1+x^2} dx$ is equal to: