Convolution of scaled variable

Question

A rather simple question...

Is the following true?

$$f * f(\frac{x}{a}) = \int_\mathbb{R} f(u)f(\frac{x}{a}-u)du$$

Or is it

$$f * f(\frac{x}{a}) = \int_\mathbb{R} f(\frac{u}{a})f(\frac{x}{a}-u)du$$

or something else...?

Answer 1

$$\int_\mathbb{R} f(u)f(\frac{x}{a}-u)du = \int_\mathbb{R} f(\frac{u}{a})f(\frac{x}{a}-\frac{u}{a})du$$

since we're integrating over $\mathbb{R}$