List of top Mathematics Questions on Integration by Partial Fractions asked in KEAM

$\int \frac{x^2 + 6x + 1}{(x+3)^2} dx = $}

For the curve \[ y = \alpha x^2 + \cos y + \beta, \] the value of \( \frac{dy}{dx} \) at \( (1,0) \) is 2. Then the value of \( \alpha \beta \) is equal to