How do you integrate $int xe^(x/2)$ using integration by parts?

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Answer 1 · 2018-04-20T18:40:26

$intxe^(x/2)dx=2e^(x/2)(x-2)+C$

Make the following selections:

$u=x$

$du=dx$

$dv=e^(x/2)dx$

$v=inte^(x/2)dx=2e^(x/2)$

Then

$uv-intvdu=2xe^(x/2)-2inte^(x/2)dx=2xe^(x/2)-4e^(x/2)+C$

Factoring out the exponential, we obtain

$intxe^(x/2)dx=2e^(x/2)(x-2)+C$

How do you integrate int xe^(x/2)int xe^(x/2) using integration by parts?