CUET Mathematics 2026 29th May Shift 2 PYQs

$\displaystyle\int \dfrac{(x-3)e^x}{(x-1)^3}dx$ is equal to:

(where C is an arbitrary constant)

$\int \frac{\sqrt{\tan x}}{\sin x \cos x} dx$ equals :

If $\frac{d}{dx}(f(x)) = 5x^4 - \frac{4}{x^5}$ such that $f(1) = 0$. Then $f(2) - 2f\left(\frac{1}{2}\right)$ is equal to :