Obtain the replacement of integral variable?

Questions
,
1

Would you like to tell me how to realize the replacement of integral variable?

Integrate[E^(-(1 - s^2)/(2 \[Epsilon])), {s, 0, -1 + \[Epsilon] x1}],
s ---> -1 + x1 \[Epsilon] + u

u is the new integral vaiable.

2

I think the result will be the same as that before replacement.

3

@Zhonghui

of course. you are absolutely right (and it must be the same!).

Look at

j1 = Integrate[E^(-(1 - s^2)/(2 \[Epsilon])), {s, 0, -1 + \[Epsilon] x1}]

and after the replacement

-(1 - s^2)/(2 \[Epsilon]) /. s -> -1 + x1 \[Epsilon] + u //   Expand // FullSimplify


j2=   Integrate[Exp[((-2 + u + x1 \[Epsilon]) (u + x1 \[Epsilon]))/(
2 \[Epsilon])] D[-1 + x1 \[Epsilon] + u, u], {u, 1 - x1 \[Epsilon],
0}]
4

But I need the second form for further calculation.

5

Well, then just copy the second form. Or what do you mean?