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review derivation: integration by parts

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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
5 declare final expr
  1. 8489593964; locally 3848329:
    \(\int u dv = u v - \int v du\)
    \(\int pdg_{4221}\, dpdg_{5177} = pdg_{4221} pdg_{5177} - \int pdg_{5177}\, dpdg_{4221}\)
no validation is available for declarations 8489593964: error for dim with 8489593964
 8489593964: N/A
2 subtract X from both sides
  1. 8489593958; locally 3494854:
    \(d(u v) = u dv + v du\)
    \(pdg_{4221}\)
  1. 0009492929:
    \(v du\)
    \(pdg_{4221} pdg_{5177}\)
  1. 8489593960; locally 2938188:
    \(d(u v) - v du = u dv\)
    \(pdg_{4221}\)
Nothing to split 8489593958:
8489593960:
8489593958:
8489593960:
3 swap LHS with RHS
  1. 8489593960; locally 2938188:
    \(d(u v) - v du = u dv\)
    \(pdg_{4221}\)
  1. 8489593962; locally 2938190:
    \(u dv = d(u v) - v du\)
    \(pdg_{4221}\)
Nothing to split 8489593960:
8489593962: no LHS/RHS split
 8489593960:
8489593962: N/A
1 declare identity
  1. 8489593958; locally 3494854:
    \(d(u v) = u dv + v du\)
    \(pdg_{4221}\)
no validation is available for declarations 8489593958:
8489593958:
4 indefinite integration
  1. 8489593962; locally 2938190:
    \(u dv = d(u v) - v du\)
    \(pdg_{4221}\)
  1. 8489593964; locally 3848329:
    \(\int u dv = u v - \int v du\)
    \(\int pdg_{4221}\, dpdg_{5177} = pdg_{4221} pdg_{5177} - \int pdg_{5177}\, dpdg_{4221}\)
Nothing to split 8489593962: no LHS/RHS split
8489593964: error for dim with 8489593964
 8489593962: N/A
8489593964: N/A
Physics Derivation Graph: Steps for integration by parts

Symbols for this derivation

See also all 227 symbols
symbol ID category latex scope dimension name value Used in derivations references
4221 variable u
\(u\)		 ['real'] dimensionless 5
5177 variable v
\(v\)		 real dimensionless none
  • str_note
2
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