Generated by the Physics Derivation Graph. Eq. \ref{eq:3494854} is an identity. $$d(u v) = u dv + v du \label{eq:3494854}$$ Subtract $$v du$$ from both sides of Eq. \ref{eq:3494854}; yields Eq. \ref{eq:2938188}. $$d(u v) - v du = u dv \label{eq:2938188}$$ Swap LHS of Eq. \ref{eq:2938188} with RHS; yields Eq. \ref{eq:2938190}. $$u dv = d(u v) - v du \label{eq:2938190}$$ Indefinite integral of both sides of Eq. \ref{eq:2938190}; yields Eq. \ref{eq:3848329}. $$\int u dv = u v - \int v du \label{eq:3848329}$$ Eq. \ref{eq:3848329} is one of the final equations.