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Review integration by parts

step inference rule input feed output step validity (as per SymPy)
1
  • 111299: declare identity
  • number of inputs: 0; feeds: 0; outputs: 1
  • Eq.~\\ref{eq:#1} is an identity.
  1. 8489593958
    \(d(u v)=u dv + v du\)
no validation is available for declarations
2
  • 111282: subtract X from both sides
  • number of inputs: 1; feeds: 1; outputs: 1
  • Subtract $#1$ from both sides of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.
  1. 8489593958
    \(d(u v)=u dv + v du\)
  1. 0009492929
    \(v du\)
  1. 8489593960
    \(d(u v) - v du=u dv\)
invalid syntax (<string>, line 0)
3
  • 111268: swap LHS with RHS
  • number of inputs: 1; feeds: 0; outputs: 1
  • Swap LHS of Eq.~\\ref{eq:#1} with RHS; yields Eq.~\\ref{eq:#2}.
  1. 8489593960
    \(d(u v) - v du=u dv\)
  1. 8489593962
    \(u dv=d(u v) - v du\)
invalid syntax (<string>, line 0)
4
  • 111608: indefinite integration
  • number of inputs: 1; feeds: 0; outputs: 1
  • Indefinite integral of both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.
  1. 8489593962
    \(u dv=d(u v) - v du\)
  1. 8489593964
    \(\int u dv=u v - \int v du\)
recognized infrule but not yet supported
5
  • 111341: declare final expression
  • number of inputs: 1; feeds: 0; outputs: 0
  • Eq.~\\ref{eq:#1} is one of the final equations.
  1. 8489593964
    \(\int u dv=u v - \int v du\)
no validation is available for declarations


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