{"id":"https://openalex.org/W4283262512","doi":"https://doi.org/10.3390/axioms11070301","title":"New Theorems in Solving Families of Improper Integrals","display_name":"New Theorems in Solving Families of Improper Integrals","publication_year":2022,"publication_date":"2022-06-21","ids":{"openalex":"https://openalex.org/W4283262512","doi":"https://doi.org/10.3390/axioms11070301"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11070301","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11070301","pdf_url":"https://www.mdpi.com/2075-1680/11/7/301/pdf?version=1656037376","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/7/301/pdf?version=1656037376","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007246366","display_name":"Mohammad Abu-Ghuwaleh","orcid":"https://orcid.org/0000-0001-5478-4785"},"institutions":[{"id":"https://openalex.org/I153687341","display_name":"Zarqa University","ror":"https://ror.org/01wf1es90","country_code":"JO","type":"education","lineage":["https://openalex.org/I153687341"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Mohammad Abu Ghuwaleh","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan","institution_ids":["https://openalex.org/I153687341"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025732055","display_name":"Rania Saadeh","orcid":"https://orcid.org/0000-0002-6394-1452"},"institutions":[{"id":"https://openalex.org/I153687341","display_name":"Zarqa University","ror":"https://ror.org/01wf1es90","country_code":"JO","type":"education","lineage":["https://openalex.org/I153687341"]}],"countries":["JO"],"is_corresponding":true,"raw_author_name":"Rania Saadeh","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan","institution_ids":["https://openalex.org/I153687341"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024913716","display_name":"Aliaa Burqan","orcid":"https://orcid.org/0000-0002-1649-1073"},"institutions":[{"id":"https://openalex.org/I153687341","display_name":"Zarqa University","ror":"https://ror.org/01wf1es90","country_code":"JO","type":"education","lineage":["https://openalex.org/I153687341"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Aliaa Burqan","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan","institution_ids":["https://openalex.org/I153687341"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025732055"],"corresponding_institution_ids":["https://openalex.org/I153687341"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.4881,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.79844441,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"11","issue":"7","first_page":"301","last_page":"301"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6551164388656616},{"id":"https://openalex.org/keywords/simplicity","display_name":"Simplicity","score":0.6033114194869995},{"id":"https://openalex.org/keywords/table","display_name":"Table (database)","score":0.5411339402198792},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5168440937995911},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5140234231948853},{"id":"https://openalex.org/keywords/maple","display_name":"Maple","score":0.4706624746322632},{"id":"https://openalex.org/keywords/trigonometric-integral","display_name":"Trigonometric integral","score":0.45490890741348267},{"id":"https://openalex.org/keywords/order-of-integration","display_name":"Order of integration (calculus)","score":0.43009430170059204},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.42392632365226746},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29780349135398865},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2787579298019409},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2079964578151703},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.06954941153526306}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6551164388656616},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.6033114194869995},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.5411339402198792},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5168440937995911},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5140234231948853},{"id":"https://openalex.org/C2780414537","wikidata":"https://www.wikidata.org/wiki/Q42292","display_name":"Maple","level":2,"score":0.4706624746322632},{"id":"https://openalex.org/C65692021","wikidata":"https://www.wikidata.org/wiki/Q1094282","display_name":"Trigonometric integral","level":3,"score":0.45490890741348267},{"id":"https://openalex.org/C38582570","wikidata":"https://www.wikidata.org/wiki/Q3825182","display_name":"Order of integration (calculus)","level":2,"score":0.43009430170059204},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.42392632365226746},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29780349135398865},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2787579298019409},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2079964578151703},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.06954941153526306},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11070301","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11070301","pdf_url":"https://www.mdpi.com/2075-1680/11/7/301/pdf?version=1656037376","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b53bbc2c95cb4092b434546c1a21826f","is_oa":true,"landing_page_url":"https://doaj.org/article/b53bbc2c95cb4092b434546c1a21826f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 7, p 301 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/7/301/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11070301","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 7; Pages: 301","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11070301","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11070301","pdf_url":"https://www.mdpi.com/2075-1680/11/7/301/pdf?version=1656037376","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283262512.pdf","grobid_xml":"https://content.openalex.org/works/W4283262512.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W2024654356","https://openalex.org/W2503073195","https://openalex.org/W2519963607","https://openalex.org/W2524008506","https://openalex.org/W2550822554","https://openalex.org/W2582064202","https://openalex.org/W2900600863","https://openalex.org/W2990424252","https://openalex.org/W3108661190","https://openalex.org/W3145989604","https://openalex.org/W3190788454","https://openalex.org/W3210208474","https://openalex.org/W3217038909","https://openalex.org/W3217323655","https://openalex.org/W4205301173","https://openalex.org/W4245626532","https://openalex.org/W4250010252","https://openalex.org/W4388295307","https://openalex.org/W6726527831","https://openalex.org/W6802645097"],"related_works":["https://openalex.org/W2626002520","https://openalex.org/W2036505231","https://openalex.org/W174892752","https://openalex.org/W2026548703","https://openalex.org/W615719172","https://openalex.org/W4230623537","https://openalex.org/W3151855842","https://openalex.org/W3129714057","https://openalex.org/W2992193318","https://openalex.org/W235560159"],"abstract_inverted_index":{"Many":[0],"improper":[1,50,89],"integrals":[2,9],"appear":[3],"in":[4,29,83,130],"the":[5,27,93,96,99,131],"classical":[6,132],"table":[7,133],"of":[8,49,58,98,134,142],"by":[10,64,114],"I.":[11,15],"S.":[12],"Gradshteyn":[13],"and":[14,95,106,124],"M.":[16],"Ryzhik.":[17],"It":[18],"is":[19],"a":[20],"challenge":[21],"for":[22,87,122],"some":[23,42,104],"researchers":[24],"to":[25,45,127,147],"determine":[26],"method":[28],"which":[30],"these":[31],"integrations":[32,59,109,123],"are":[33,81],"formed":[34],"or":[35,70,145],"solved.":[36],"In":[37,52,72],"this":[38,73],"article,":[39,74],"we":[40,54,75,102,118],"present":[41,76,103],"new":[43,56,85,120,149],"theorems":[44,79],"solve":[46],"different":[47],"families":[48],"integrals.":[51,90,150],"addition,":[53],"establish":[55],"formulas":[57,86],"that":[60,80,110,128],"cannot":[61,111],"be":[62,112],"solved":[63,113],"mathematical":[65],"software":[66],"such":[67],"as":[68],"Mathematica":[69],"Maple.":[71],"three":[77],"main":[78],"essential":[82],"generating":[84],"solving":[88],"To":[91],"show":[92],"efficiency":[94],"simplicity":[97],"presented":[100],"techniques,":[101],"applications":[105],"examples":[107],"on":[108],"regular":[115],"methods.":[116],"Furthermore,":[117],"acquire":[119,148],"results":[121],"compare":[125],"them":[126],"obtained":[129],"integrations.":[135],"Some":[136],"previous":[137],"results,":[138],"become":[139],"special":[140],"cases":[141],"our":[143],"outcomes":[144],"generalizations":[146]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-06-23T00:00:00"}