A. ∫ (4 + x)-½x²)dx =

[tex] \int \: 4 + x - \frac{1}{2} {x}^{2} = \\ = - \int \frac{ {x}^{2} }{2} dx + \int \: xdx + \int4dx \\ = - \frac{ {x}^{3} }{2} + \frac{ {x}^{2} }{2} + 4x \\ = - \frac{ {x}^{3} }{6} + \frac{ {x}^{2} }{2} + 4x + c[/tex]