### Solved: Why does integrate(psi(y)*f(y),y) return an error but integrate(psi(t,y)*f(t,y),y) works?

*Symbolic Integration works only with second dummy variable*

Hi there,

I am trying get an symbolic expression for the convolution
$$ (\psi \star f)(x) := \int\limits_{\mathbb{R}} \psi(x-y) f(y) {d y} $$

of two functions
$
f, \psi: \mathbb{R} \to \mathbb{R}
$
as follows:

```
var('y')
```

psi = function('psi')(y)

f = function('f')(y)

integrate(psi(x-y)*f(y),y)

upon which I get the error message

RuntimeError: ECL says: Error executing code in Maxima:

If I add an extra argument to the two functions and define them as
$$ f, \psi : \mathbb{R} \times \mathbb{R} \to \mathbb{R} $$
as follows:

```
var('t')
```

psi = function('psi')(t,y)

f = function('f')(t,y)

integrate(psi(t,x-y)*f(t,y),y)

there is a surprise, *it suddenly works!*
I get the desired symbolic expression on which I can run diff(..,x) and all the other built-in functions.

**TL;DR**
Why does `integrate(psi(y)*f(y),y)`

return an error?

~~What am I missing here ?~~Solution
Use sympy backend for symbolic integration as in
`integrate(psi(x-y)*f(y),y, algorithm="sympy")`