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Review integration by parts

abstract:
reference:

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111299: declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an identity.			8489593958 $d(u v) = u dv + v du$	no validation is available for declarations
2	0000111282: 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}.	8489593958 $d(u v) = u dv + v du$	0009492929 $v du$	8489593960 $d(u v) - v du = u dv$	Not evaluated due to missing term in SymPy
3	0000111268: 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}.	8489593960 $d(u v) - v du = u dv$		8489593962 $u dv = d(u v) - v du$	Not evaluated due to missing term in SymPy
4	0000111608: 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}.	8489593962 $u dv = d(u v) - v du$		8489593964 $\int u dv = u v - \int v du$	recognized infrule but not yet supported
5	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	8489593964 $\int u dv = u v - \int v du$			no validation is available for declarations

Symbols used in integration by parts

0000004221: $ u $
0000005177: $ v $

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timing of Neo4j queries:

0.012 seconds for pdg_app/to_review_derivation 4b8f0c23-c5a0-43b0-bc58-7e11f9b0978b
0.007 seconds for compute/get_dict_of_steps_in_derivation: steps_in_this_derivationaaf71dd9-a1f5-4954-9444-073120b22f32
0.008 seconds for compute/input_feed_output_infrule_for_step: get_inference_rule_connected_to_step_IDaaf71dd9-a1f5-4954-9444-073120b22f32
0.009 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type HAS_INPUTaaf71dd9-a1f5-4954-9444-073120b22f32
0.01 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_FEEDaaf71dd9-a1f5-4954-9444-073120b22f32
0.012 seconds for compute/input_feed_output_infrule_for_step: get_expressions_from_step_id_and_expr_type, HAS_OUTPUTaaf71dd9-a1f5-4954-9444-073120b22f32
0.011 seconds for compute/get_dict_of_steps_in_derivation: get_sequence_index_for_stepaaf71dd9-a1f5-4954-9444-073120b22f32
0.004 seconds for pdg_app/ 4b8f0c23-c5a0-43b0-bc58-7e11f9b0978b

step	inference rule	input	feed	output	step validity (as per SymPy)
1	0000111299: declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\ref{eq:#1} is an identity.			8489593958 \(d(u v) = u dv + v du\)	no validation is available for declarations
2	0000111282: 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}.	8489593958 \(d(u v) = u dv + v du\)	0009492929 \(v du\)	8489593960 \(d(u v) - v du = u dv\)	Not evaluated due to missing term in SymPy
3	0000111268: 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}.	8489593960 \(d(u v) - v du = u dv\)		8489593962 \(u dv = d(u v) - v du\)	Not evaluated due to missing term in SymPy
4	0000111608: 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}.	8489593962 \(u dv = d(u v) - v du\)		8489593964 \(\int u dv = u v - \int v du\)	recognized infrule but not yet supported
5	0000111341: declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\ref{eq:#1} is one of the final equations.	8489593964 \(\int u dv = u v - \int v du\)			no validation is available for declarations