fine the most general anti derivative of the function check your answer by differentiation

Question

3) f(x) = (2 + x - x ^ 2)/(sqrt(x))

Answer 1

f(x) = (2 + x - x²)/√x

f(x) = 2/√x + x/√x - x²/√x

f(x) = 2x^-1/2 + x^(1-1/2) - x^{(2 - 1/2)}

f(x) = 2x^-1/2 + x^1/2 - x^3/2

So the antiderivative (going backwards from the derivative power rule) of f(x) is 4x^1/2 + 2/3x^3/2 - 2/5x^5/2 + C