One may apply integration by parts for any identification of the integrand as $uv'$, but since we're left with another integral with integrand $u'v$, it is wise to choose some $v'$ that is easily integrated into $v$ and some $u$ that is easily differentiated into $u'$. In our previous example we had

and both $u'$ and $v$ are simple enough for the change to be advantageous