How do you integrate $\int r e^{\frac{r}{2}}$ $int re^(r/2)$ by integration by parts method?

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How do you integrate $\int r e^{\frac{r}{2}}$ $int re^(r/2)$ by integration by parts method?

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Answer 1 · 2016-10-20T12:50:05

$\int r e^{\frac{r}{2}} d r = (2 r - 4) e^{\frac{r}{2}} + C$ $intre^(r/2)dr=(2r-4)e^(r/2)+C$

Explanation:

Let $u = r$ $u=r$ then $u'=1$
and $v'=e^(r/2)$ then $v=2e^(r/2)$
$intuv'=uv-intu'v$
so $intre^(r/2)dr=2re^(r/2)-int2e^(r/2)dr$
$=2re^(r/2)-2*2e^(r/2)$
$=2re^(r/2)-4e^(r/2)+C$
$=(2r-4)e^(r/2)+C$

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How do you integrate $\int r e^{\frac{r}{2}}$ $int re^(r/2)$ by integration by parts method?

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