Dadas $A={\displaystyle \underset{0}{\overset{1}{}}}{e}^{-t^2}dt$ y $B={\displaystyle \underset{0}{\overset{\frac{1}{2}}{}}}{e}^{-t^2}dt.$ Calcular la integral reiterada

$I=2{\displaystyle \underset{-\frac{1}{2}}{\overset{1}{}}}[{\displaystyle \underset{0}{\overset{x}{}}}{e}^{-y^2}dy]dx$

En funci$$n de $A$ y $B.$ Existen enteros positivos $m$ y $n$ tales que

$I=mA-nB+e^{-1}-e^{-\frac{1}{4}}$

Calcular la integral doble

${\displaystyle \underset{1}{\overset{2}{}}}[{\displaystyle \underset{0}{\overset{logx}{}}}(x-1)\sqrt[\phantom{2}]{1+e^{2y}}dy]dx$