Hi I am having difficulty integrating the following differential equation, its for use in a runge kutta numerical analysis. I know how to perform the RK algorithm but I am struggling with possibly the easiest part which is the initial integration.

x1 = dx/dt = xt

and this is how far I have got;

\int dx/x = \int t.dt

lnx = t.t + c

Can anyone correct me if i'm wrong so far and help me finish of the integration please.

Much appreciated