Antiderivative of (2x + 3x^2)/x

int (3x^2 + 2x)/x dx
= int (3x + 2) dx
= 3x^2/2 + 2x

You can furthur simplify that function before you anti-derive it.
It's equivalent to 2+3x
The anti-derivative of that is 2x + 1.5x^2

2x+(3/2)x^2 + C