Sorry, but it's been a while since I've done calculus.
Evaluate the integral:
$\displaystyle \int re^{r/2}dr$
Do you let $\displaystyle u = r$ and $\displaystyle dv = e^{r/2}dr$?
From there, I'm not sure what to do.
Hello, cinder!
Evaluate the integral: .$\displaystyle \int re^{\frac{r}{2}}dr$
Do you let: $\displaystyle u = r$ and $\displaystyle dv = e^{\frac{r}{2}}dr$? . . . . Yes!
Integration by parts . . .
. . $\displaystyle \begin{array}{ccc}u = r & dv = e^{\frac{r}{2}}dr \\ du = dr & v = 2e^{\frac{r}{2}} \end{array}$
And we have: .$\displaystyle 2re^{\frac{r}{2}} - 2\int e^{\frac{r}{2}}\,dr \;=\;2re^{\frac{r}{2}} - 4e^{\frac{r}{2}} + C \;=\;2e^{\frac{r}{2}}(r - 2) + C$