[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522890-105":59,"doc-detail-522890-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","integration-by-substitution-calculus-worksheet","Integration by Substitution - Calculus Worksheet","","This calculus worksheet provides a series of practice problems focused on solving indefinite integrals using the method of integration by substitution. The document includes specific exercises requiring the application of provided substitution variables, as well as general problems involving various trigonometric and logarithmic functions. Designed for educational purposes, it serves as an assessment tool for students to master integration techniques, providing both the problem statements and their corresponding evaluated solutions to facilitate independent learning and practice.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/integration-by-substitution-calculus-worksheet/522890/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/integration-by-substitution-calculus-worksheet/522890.png","ImageObject",300,407,{"name":92,"@type":93},"Fahsai","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the primary method used to solve these integrals?","Question",{"text":113,"@type":114},"The primary method demonstrated in this worksheet is integration by substitution, where a variable 'u' is assigned to a part of the integrand to simplify the expression.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"Are the solutions provided for the practice problems?",{"text":118,"@type":114},"Yes, the document includes an answer key section following the problem sets, providing the evaluated indefinite integrals with the constant of integration 'C'.",{"name":120,"@type":111,"acceptedAnswer":121},"What types of functions are involved in these integration problems?",{"text":122,"@type":114},"The problems involve a variety of functions, including algebraic, logarithmic, and trigonometric functions such as sine, cosine, cotangent, and cosecant.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},522890,1791492331,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":24,"preview_page_count":4},549768702563,"https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083","Kuta Software-Infinite Calculus Name   \nIntegration by Substitution Date  Period   \nEvaluate each indefinite integral. Use the provided substitution.  \n1) ∫~~ ~~2532~~ ~~ dx; u = 5x4 2) ∫ ~~ ~~9~~ ~~0x44x10~~ ~~ dx; u = 2x5  \n3) ∫ − ~~ ~~cot~~ ~~(2x2)~~ ~~~~ ~~csc2co2xt~~ ~~2~~ ~~ dx; u = cot 2x 4) ∫ ~~ ~~x~~ ~~1(ln~~ ~~−2x)~~ ~~2 dx; u = ln −2x  \nEvaluate each indefinite integral.  \n5) ∫ ~~ ~~9~~ ~~x16x4~~ ~~ dx 6) ∫ ~~ ~~x~~ ~~3~~ ~~3xx26~~ ~~ dx  \n7) ∫ ~~ ~~16~~ ~~0x25x4~~ ~~ dx 8) ∫ − ~~ ~~4n~~ ~~4xcos2~~ ~~ dx  \nKuta Software-Infinite Calculus Name   \nIntegration by Substitution Date  Period   \nEvaluate each indefinite integral. Use the provided substitution.  \n1) ∫~~ ~~2532~~ ~~ dx; u = 5x4  \n−1 5x4 sin  5  + C  \n2) ∫ ~~ ~~9~~ ~~0x44x10~~ ~~ dx; u = 2x5  \n13 ⋅ tan −1 2x35~~ ~~ + C  \n3) ∫ − ~~ ~~cot~~ ~~(2x2)~~ ~~~~ ~~csc2co2xt~~ ~~2~~ ~~ dx; u = cot 2x 4) ∫ ~~ ~~x~~ ~~1(ln~~ ~~−2x)~~ ~~2 dx; u = ln −2x  \nsec −1  cot 2x  + C ln −2x  \nsin −1  5  + C  \nEvaluate each indefinite integral.  \n5) ∫ ~~ ~~9~~ ~~x16x4~~ ~~ dx 6) ∫ ~~ ~~x~~ ~~3~~ ~~3xx26~~ ~~ dx  \n4x2 sec −1  x 3  + C sin −1  3  + C  \n7) ∫  1146 0x25an− x145dxx24 + C 8) ∫ −sin−1 ncs34xos24x xCdx  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaimsUTrJxPCPL","https://ap.wps.com/l/cbCaimsUTrJxPCPL","pdf",30455,"English","# Practice Problems\n## Exercises with Suggested Substitution\n## General Indefinite Integrals","[{\"question\":\"What is the primary method used to solve these integrals?\",\"answer\":\"The primary method demonstrated in this worksheet is integration by substitution, where a variable 'u' is assigned to a part of the integrand to simplify the expression.\"},{\"question\":\"Are the solutions provided for the practice problems?\",\"answer\":\"Yes, the document includes an answer key section following the problem sets, providing the evaluated indefinite integrals with the constant of integration 'C'.\"},{\"question\":\"What types of functions are involved in these integration problems?\",\"answer\":\"The problems involve a variety of functions, including algebraic, logarithmic, and trigonometric functions such as sine, cosine, cotangent, and cosecant.\"}]","Integration by Substitution - Calculus Worksheet | PDF",1791426279]