[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-572889-105":3,"detail-sidebar-cat-1-en-105":81,"doc-detail-572889-en":127},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","integrals-cheat-sheet-common-integrals","Integrals Cheat Sheet - Common Integrals","","Symbolab Integrals Cheat Sheet compiles compact reference formulas for solving calculus integrals. It lists common integral results, trigonometric and inverse trigonometric integrals, hyperbolic integrals, and integrals involving special functions such as Ei, Si, Ci, and error-related forms. The sheet also summarizes indefinite and definite integration rules, including integration by parts, constant and power rules, substitution, and techniques for evaluating definite integrals with boundaries, odd functions, discontinuities, and defined-point cases.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/presentations/","Presentations",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/integrals-cheat-sheet-common-integrals/572889/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/integrals-cheat-sheet-common-integrals/572889.png","ImageObject",442,249,{"name":42,"@type":43},"Ophelia","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-20","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",7,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What kinds of integrals are covered in the sheet?","Question",{"text":63,"@type":64},"It covers common integrals, trigonometric and inverse trigonometric integrals, hyperbolic integrals, and integrals of special functions such as Ei, Si, Ci, Shi, and Chi.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which rules for indefinite integrals are included?",{"text":68,"@type":64},"It includes integration by parts, constant and factoring rules, sum/difference, adding a constant to the result, the power rule, and substitution.",{"name":70,"@type":61,"acceptedAnswer":71},"How does the sheet handle definite integrals?",{"text":72,"@type":64},"It provides rules for boundary handling with limits, properties for odd functions, treatment of undefined points using interval splitting, and the case of an integral with a defined point where the value can be zero.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},572889,1792022767,{"code":4,"msg":82,"data":83},"success",[84,88,93,98,103,108,113,118,123],{"id":85,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":86,"slug":87},11,90,"presentations",{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},12,"Resumes",80,"resumes",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},14,"Invoices",70,"invoices",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},15,"Posters",60,"posters",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},16,"Social Media",50,"social-media",{"id":109,"doc_module":22,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},17,"Forms",40,"forms",{"id":114,"doc_module":22,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},18,"Letters",30,"letters",{"id":119,"doc_module":22,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},21,"Paper Templates",5,"papers-templates",{"id":124,"doc_module":22,"doc_module_name":25,"category_name":125,"show_sort_weight":4,"slug":126},158,"General","general-158",{"code":4,"msg":82,"data":128},{"doc_id":79,"user_id":129,"nickname":42,"user_avatar":130,"doc_module":22,"category_id":85,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":26,"language":136,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":12,"update_tm":140,"read_time":22},7971461741311,"https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826","Symbolab Integrals Cheat Sheet  \nCommon Integrals:  \n􀁸 ∫ 􀝔−1􀝀􀝔 = ln (􀝔)  \n􀁸 ∫ 􀯗􀯫􀯫 = ln (􀝔)   \n􀁸 ∫|􀝔|􀝀􀝔 = 􀯫􀯫~~ ~~2  \nTrigonometric Integrals:  \n􀁸 ∫ sec2 (􀝔) 􀝀􀝔 = tan (􀝔)  \n􀁸 ∫ csc2 (􀝔) 􀝀􀝔 = − cot(􀝔)  \nArc Trigonometric Integrals:  \n􀁸 ∫ 􀯫~~ ~~􀯗21 = arctan (􀝔)  \n􀁸 ∫ √􀯫~~ 2~~ = arcsin (􀝔)  \n􀁸 ∫ √􀯫~~ 2~~ 􀝀􀝔 = arccos (􀝔)  \n􀁸 ∫ 􀯫~~ ~~−21 􀝀􀝔 = arccot (􀝔)  \n􀁸 ∫ ~~ ~~|􀯫|~~2 ~~−1 􀝀􀝔 = arccsc (􀝔)  \nHyperbolic Integrals:  \n􀁸 ∫ sech2 (􀝔) 􀝀􀝔 = tanh (􀝔)  \n􀁸 ∫ csch2 (􀝔) 􀝀􀝔 = − coth(􀝔)  \n􀁸 ∫ cosh(􀝔) 􀝀􀝔 = sinh (􀝔)  \nIntegrals of Special Functions:  \n􀁸 ∫ cos (􀯫~~ ~~22􀰗) 􀝀􀝔 = 􀜥 (􀝔)  \n􀁸 ∫ sin􀯫(􀯫) 􀝀􀝔 = Si (􀝔)  \n􀁸 ∫ cos􀯫(􀯫) 􀝀􀝔 = Ci (􀝔)  \n􀁸 ∫ sinh􀯫(􀯫) 􀝀􀝔 = Shi (􀝔)  \n􀁸 ∫ cosh􀯫(􀯫) 􀝀􀝔 = Chi (􀝔)  \n􀁸 ∫ 􀯘􀳣􀯫 􀝀􀝔 = Ei (􀝔)  \n􀁸 ∫ 􀝁 􀯫 􀝀􀝔 = 􀝁 􀯫  \n􀁸 ∫ sin(􀝔) 􀝀􀝔 = − cos(􀝔)  \n􀁸 ∫ cos(􀝔) 􀝀􀝔 = sin (􀝔)  \n􀁸 ∫ si􀯗n􀯫2(􀯫) = − cot(􀝔)  \n􀁸 ∫ co􀯗s􀯫2(􀯫) tan (􀝔)  \n􀁸 ∫ ~~ ~~|􀯫|􀯫~~2 ~~−1 = arcsec (􀝔)  \n􀁸 ∫ 1􀯫􀯫2 = arctanh (􀝔)  \n􀁸 ∫ √􀯫􀯗1 = arcsinh (􀝔)  \n􀁸 ∫ ~~ ~~|􀯫|􀯫~~2 ~~+1 = − arccsch(􀝔)  \n􀁸 ∫ sinh(􀝔) 􀝀􀝔 = cosh (􀝔)  \n􀁸 ∫ csch(􀝔) 􀝀􀝔 = ln (tanh (􀯫2))  \n􀁸 ∫ sec(􀝔) 􀝀􀝔 = ln (tan(􀝔) + sec(􀝔))  \n􀁸 ∫ 􀝁 −􀯫2 􀝀􀝔 =  erf(􀝔)  \n􀁸 ∫ 􀝁 􀯫 2 􀝀􀝔 = 􀝁 􀯫 2 F (􀝔)  \n􀁸 ∫ sin (􀯫~~ ~~22􀰗) 􀝀􀝔 = S (􀝔)    \n􀁸 ∫ sin(􀝔2) 􀝀􀝔 = √􀰗2 S (√2􀰗 􀝔 )  \n􀁸 ∫ l􀯗n(􀯫􀯫) = li (􀝔)  \nIndefinite Integrals Rules:  \n􀁸 Integration By Parts: ∫ 􀝑􀝒′ = 􀝑􀝒 − ∫ 􀝑′􀝒  \n􀁸 Integral of a Constant: ∫ 􀝂(􀜽)􀝀􀝔 = 􀝔 ⋅ 􀝂(􀜽)  \n􀁸 Taking a Constant out: ∫ 􀜽 ⋅ 􀝂(􀝔)􀝀􀝔 = 􀜽 ⋅ ∫ 􀝂(􀝔)􀝀􀝔  \n􀁸 Sum/Difference Rule: ∫ 􀝂(􀝔) ± 􀝃 (􀝔)􀝀􀝔 = ∫ 􀝂(􀝔)􀝀􀝔 ± ∫ 􀝃 (􀝔)􀝀􀝔  \n􀁸 Add a Constant to the Solution: If 􀯗􀮿􀯗(􀯫􀯫) = 􀝂 (􀝔), then ∫ 􀝂(􀝔)􀝀􀝔 = 􀜨 (􀝔) + 􀜥  \n􀁸 Power Rule: ∫ 􀝔􀯔 􀝀􀝔 = 􀯫􀯔11 , 􀜽 ≠ −1  \n􀁸 Integral Substitution: ∫ 􀝂(􀝃 (􀝔)) ⋅ 􀝃′(􀝔)􀝀􀝔 = ∫ 􀝂(􀝑)􀝀􀝑 , 􀝑 = 􀝃 (􀝔)  \nDefinite Integrals Rules:  \n􀁸 Definite Integral Boundaries: ∫􀯕􀯔 􀝂 (􀝔)􀝀􀝔 = 􀜨 (􀜾) − 􀜨(􀜽) = lim􀯫→􀯕− 􀜨(􀝔) − lim􀯫→􀯔+ 􀜨 (􀝔)  \n􀁸 Odd Function: If 􀝂(􀝔) = −􀝂(−􀝔), then ∫􀯔 􀝂 (􀝔)􀝀􀝔 = 0  \n􀁸 Undefined Points: If 􀜽 \u003C 􀜾 \u003C 􀜿, and 􀝂(􀜾) is undefined, then ∫􀯖􀯔 􀝂 (􀝔)􀝀􀝔 =∫􀯕􀯔 􀝂 (􀝔)􀝀􀝔 + ∫􀯕􀯖 􀝂 (􀝔)􀝀􀝔  \n􀁸 Definite Integral of a defined point: ∫􀯔􀯔 􀝂 (􀝔)􀝀􀝔 = 0","cbCaijS2OLbvKyPN","https://ap.wps.com/l/cbCaijS2OLbvKyPN","pdf",455179,"English","# Common Integrals\n# Trigonometric Integrals\n# Arc Trigonometric Integrals\n# Hyperbolic Integrals\n# Integrals of Special Functions\n# Indefinite Integrals Rules\n## Integration by Parts\n## Indefinite Rules\n# Definite Integrals Rules\n## Boundaries and Limits\n## Properties and Edge Cases","[{\"question\":\"What kinds of integrals are covered in the sheet?\",\"answer\":\"It covers common integrals, trigonometric and inverse trigonometric integrals, hyperbolic integrals, and integrals of special functions such as Ei, Si, Ci, Shi, and Chi.\"},{\"question\":\"Which rules for indefinite integrals are included?\",\"answer\":\"It includes integration by parts, constant and factoring rules, sum/difference, adding a constant to the result, the power rule, and substitution.\"},{\"question\":\"How does the sheet handle definite integrals?\",\"answer\":\"It provides rules for boundary handling with limits, properties for odd functions, treatment of undefined points using interval splitting, and the case of an integral with a defined point where the value can be zero.\"}]","Integrals Cheat Sheet - Common Integrals | PDF",1791929910]