What is the integral of ln x dx

as ln x is not a standard integral given in the formula booklet, but it’s derivative is a standard derivative, you can split ln x into 1 times ln x. This allows you to use the integral product rule method where the total integral is equal to uv - the integral of v(du/dx). Here you would let u = lnx and dv/dx = 1. Therefore you would differentiate u and integrate dv/dx to give du/dx = 1/x and v = x. now using these values you put them into the equation giving xlnx - the integral of x/x (vdu/dx). This finally results in Xlnx - x.