The coefficient of $x^2$ in $(3x+x^3)(x+\frac{1}{x})$ is

The correct option is C: $4$

The coefficient of a variable is the quantity multiplied with that variable.

$(3x+x^3)(x+\frac{1}{x})$

$=3x(x+\frac{1}{x})+x^3(x+\frac{1}{x})$

$=3x^2+3+x^4+x^2$

$=x^4+4x^2+3$

So, $4$ is the coefficient of $x^2$.

hence, $C$ is correct.