## 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

$$v$$
$$u$$