# Mysterious step while solving ODE

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 $\tau$?

-

If $\tau(x) = \displaystyle \int_{0}^x \kappa(y) dy$, then $d \tau = \kappa(x) dx$
$$\frac{dI}{dx}=\frac{dI}{d\tau}\frac{d\tau}{dx}=\frac{dI}{d\tau}\kappa(x).$$