$f(x)=\int x d x$

Step 1 ：The problem is asking for the integral of x with respect to x. The integral of a function is the area under the curve of the function. In this case, the function is simply x, which is a straight line.

Step 2 ：The integral of x with respect to x is \(\frac{1}{2}x^2\).

Step 3 ：Final Answer: \(\boxed{\frac{1}{2}x^2}\)