solve the integral of (r)(e^(r/2))dr
i got (2re^(r/2) - e^(r/2))/4 + C
..but that's not right.
Can you please explain or show me the correct procedure.
Looking at your answer makes me think you did a small silly mistake in the second integral of integration by parts.
$\displaystyle \int r e^{\frac{r}2} \, dr = r \dfrac{e^{\frac{r}2}}{\frac12} - \int \dfrac{e^{\frac{r}2}}{\frac12}\, dr $$\displaystyle = 2r e^{\frac{r}2} - \int 2e^{\frac{r}2} \, dr = 2r e^{\frac{r}2} - 2\dfrac{e^{\frac{r}2}}{\frac12} = 2r e^{\frac{r}2} - 4e^{\frac{r}2} $