`f(x) = e^x + root(3)(x)`

Let F(x) be the anti derivative of f(x).

To determine F(x), take the integral of f(x).

`F(x) = int f(x) dx = int (e^x + root(3)(x) ) dx = int e^xdx + int root(3)(x)dx`

To integrate the first term, apply the exponential formula `int e^u du = e^u + C` .

`= e^x + C + int root(3)(x) dx`

For the second term, express the radical as exponent. Then ,apply the power formula of integral which is `int u^n du = u^(n+1)/(n+1) + C ` .

`= e^x + C + int x^(1/3)dx`

`= e^x + C + x^ (4/3) /(4/3) + C`

`= e^x + C + (3x^(4/3))/ 4 + C`

Since C represents any number, we may re-write C + C as C only.

`= e^x + (3x^(4/3))/4 + C`

**Hence, the anti derivative of `f(x) = e^x + roo(3)(x)` is `F(x)=e^x + (3x^(4/3))/4 + C` .**