integration by parts

$\int (f\times g{)}^{\prime }dx$
$=\int (f^{\prime }\times g)dx+\int (f\times g^{\prime })dx$

$f\times g$
$=\int f^{\prime }\times gdx+\int f\times g^{\prime }dx$
$\Rightarrow \int f\times g^{\prime }dx=f\times g-\int f^{\prime }\times gdx$