Following the change of variable thread, I wanted to streamline the whole process.

Namely, using the same example in the above thread, I'd like to say

```
integral_def_change(x*cos(x^2+1), (x, 0, 2*pi), u==x^2+1, u)
```

The difference is, I wanted also Sage to automatically solve for x instead of providing x= sqrt(u-1), say. But when I tried

```
solve(u==x^2+1, x)[0].rhs()
```

the output was `r1`

???

1- What exactly is r1 ??

A way out (see this thread) seems to make of the solution a function of `u`

```
f(u)=solve(u==x^2+1, x)[0].rhs()
```

Now f is

```
u |--> -sqrt(u - 1)
```

2- What can I do to get +sqrt(u - 1) instead? Is this related to the positive function question there?