I can 'explain' how the substitution works but actually it is not the explanation , i am going to change the integral to a form which is more intuitive .

Before this , let me ask you about another integral :

Intuition or experiences or your friend tell you to subsitute so we have

so

Here is another one :

Again , they tell us to subsitute

so

The tricks of the above two integrals are very similar , what we do is to 'reflect' the integrand to obtain the answers . But we can't explain why one could think of , our intuition always cannot be explained .

This one is very similar .

Sub.

we have

Again , sub You may find that it is equivalent to sub at the begining as

Therefore ,

so

You see , these three integrals are not different at all so if you are asking how this works , let me ask you how this also works when applied in the first two integrals .