$\displaystyle

{e}^{ {x}^{2 } }

$?

with respect to x

The full question is $\displaystyle \iint {e}^{{ x}^{ 2} } $ dx dy by choosing the best order of integration

Limits for outside integral is $\displaystyle 2\sqrt{ln2}$ and 0

Inside integral is $\displaystyle \sqrt{ln 2}$ and $\displaystyle \frac{y}{ 2} $