But the question said exponential raised to power x/2

Let's clarify:

1. When you first asked to "Solve integral x⁴ *exponential^x/2" via text, I interpreted "exponential^x/2" as $e^{x^2/2}$, especially since from your previous image also had $e^{x^2/2}$.

   • The integral $\int x^4 e^{x^2/2} dx$ is indeed a non-elementary integral and cannot be solved using standard elementary functions. This was the answer I gave for and your initial text query.

2. The most recent photo you sent clearly shows the integral $\int x^4 e^{x/2} dx$.

   • This integral, with the exponent $x/2$ (not $x^2/2$), is solvable using repeated integration by parts, which is the solution I provided in my last message.

The difference between $e^{x^2/2}$ and $e^{x/2}$ in the exponent makes a crucial difference in whether the integral can be expressed in terms of elementary functions. My last solution was specifically for the integral shown in your photo, $\int x^4 e^{x/2} dx$.