(1) (u*v)' = u'*v + u*v',it can solve a great many integrations.

To derive the formula, rewrite (1) as

(2) u'*v = (u*v)' - u*v'.Integrating both sides, we see that

(3) integral u'*v dx = u*v - integral u*v' dxwhere we hope

`u*v'`is easier to integrate than

`u'*v`.

A more concise way of writing (3) is to use the formal notation `du=u'dx`, `dv=v'dx`, and use that to re-write (3) as

(4) integral v du = u*v - integral u dv