Mathematics

The key is recognizing that $x$ and $e^{x^2}$ are intimately connected through the chain rule: the derivative of $e^{x^2}$ is $2xe^{x^2}$. This means $x\,dx$ is almost a differential of the exponent. Treat $e^{x^2}$ as your new variable and watch how the pieces align—the $x$ factor becomes part of the differential, leaving you with a simpler integral in terms of a single function.

The key is recognizing that $x$ and $e^{x^2}$ are intimately connected through the chain rule: the derivative of $e^{x^2}$ is $2xe^{x^2}$. This means $x\,dx$ is almost a differential of the exponent. Treat $e^{x^2}$ as your new variable and watch how the pieces align—the $x$ factor becomes part of the differential, leaving you with a simpler integral in terms of a single function.