I just read a paper in which an ODE was solved using a step I don't understand.
$${dI \over \kappa (x) dx} = I$$
Let
$$\tau = \int_0^x \kappa(x)dx$$
Rewrite equation as
$${dI \over d\tau} = I$$
and solve.
How does the final expression follow from the definition of $\tau$?