Mathematics

This is a substitution problem where the exponent $x^2$ is your signal that a change of variables will simplify things. Notice that the derivative of $x^2$ is $2x$, and you have an $x$ sitting right there in front of $e^{x^2}$—that's not a coincidence. Let $u = x^2$, adjust $dx$ accordingly, and watch the integral transform into a much simpler exponential form.

This is a substitution problem where the exponent $x^2$ is your signal that a change of variables will simplify things. Notice that the derivative of $x^2$ is $2x$, and you have an $x$ sitting right there in front of $e^{x^2}$—that's not a coincidence. Let $u = x^2$, adjust $dx$ accordingly, and watch the integral transform into a much simpler exponential form.