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It includes exercises requiring specific u-substitutions for logarithmic and exponential functions, as well as general problems for students to determine the appropriate substitution independently. The document is designed for academic skill-building, covering logarithmic, exponential, and trigonometric integral forms, and serves as a comprehensive study resource for students mastering integral calculus techniques.","Kuta Software-Infinite Calculus Name___________________________________  \nIntegration by Substitution Date________________ Period____  \nEvaluate each indefinite integral. Use the provided substitution.  \n1) ∫ ~~ ~~420x53~~ ~~ dx; u = 4x5 + 3 2) ∫ 36x2 e4x3 + 3 dx; u = 4x3 + 3  \n3) ∫ 80x3 ⋅ 35x4 − 2 dx; u = 5x4 − 2 4) ∫ ~~ ~~x(−1~~ ~~+2ln~~ ~~4x) dx; u = −1 + ln 4x  \nEvaluate each indefinite integral.  \n5) ∫ ~~ ~~1x3222~~ ~~ dx 6) ∫ ~~ ~~20e~~ ~~5xx3 dx  \n7) ∫ 10sin −2x ⋅ ecos −2x dx 8) ∫ ~~ ~~5e−3+x~~ ~~ln~~ ~~3x~~ ~~ dx  \nKuta Software-Infinite Calculus Name   \nIntegration by Substitution Date  Period   \nEvaluate each indefinite integral. Use the provided substitution.  \n1) ∫ ~~ ~~420x53~~ ~~ dx; u = 4x5 + 3  \nln  4x5 + 3  + C  \n2) ∫ 36x2 e4x3 + 3 dx; u = 4x3 + 3  \n3e4x3 + 3 + C  \n3) ∫ 80x3 ⋅ 35x4 − 2 dx; u = 5x4 − 2 4) ∫ ~~ ~~x(−1~~ ~~+2ln~~ ~~4x) dx; u = −1 + ln 4x  \n4 ⋅ 35x4 − 2 2 ln  −1 + ln 4x  + C ~~ ~~ + C  \nln 3  \nEvaluate each indefinite integral.  \n5) ∫ ~~ ~~1x3222~~ ~~ dx  \n4 ln  2x3 + 4  + C  \n7) ∫ 10sin −2x ⋅ ecos −2x dx  \n5ecos −2x + C  \n6) ∫ ~~ ~~20e~~ ~~5xx3 dx  \n4 ln  e 5x + 3  + C  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaioEwBcZ6VP2s","https://ap.wps.com/l/cbCaioEwBcZ6VP2s","pdf",29810,13,"English","en",105,"# Integration by Substitution Practice\n## Guided Substitution Exercises\n## General Indefinite Integrals","[{\"question\":\"What technique is primarily used to solve the problems in this worksheet?\",\"answer\":\"The worksheet focuses on the method of integration by substitution, where a variable 'u' is used to simplify complex integrals into solvable forms.\"},{\"question\":\"What types of functions are covered in these integration exercises?\",\"answer\":\"The problems involve a variety of functions, including polynomial, exponential, natural logarithmic, and trigonometric functions.\"},{\"question\":\"Are the solutions provided for the practice problems?\",\"answer\":\"Yes, the document provides the evaluated indefinite integrals for both the guided substitution problems and the independent exercises.\"}]","Integration by Substitution - Calculus Worksheet | PDF",1791426285,{"code":4,"msg":81,"data":82},"ok",{"site_id":75,"language":74,"slug":83,"title":65,"keywords":84,"description":66,"schema_data":85,"social_meta":139,"head_meta":141,"extra_data":143,"updated_unix":144},"integration-by-substitution-calculus-worksheet","",{"@graph":86,"@context":138},[87,101,121],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,99],{"item":91,"name":92,"@type":93,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":9,"@type":93,"position":14},"https://docshare.wps.com/document/",{"item":97,"name":20,"@type":93,"position":98},"https://docshare.wps.com/document/exam/",3,{"item":100,"name":65,"@type":93,"position":19},"https://docshare.wps.com/document/integration-by-substitution-calculus-worksheet/522898/",{"url":100,"name":65,"@type":102,"image":103,"author":108,"headline":65,"publisher":110,"fileFormat":113,"inLanguage":74,"description":66,"dateModified":114,"datePublished":115,"encodingFormat":113,"isAccessibleForFree":116,"interactionStatistic":117},"DigitalDocument",{"url":104,"@type":105,"width":106,"height":107},"https://docshare.wps.com/thumbnails/integration-by-substitution-calculus-worksheet/522898.png","ImageObject",300,407,{"name":63,"@type":109},"Person",{"url":91,"name":111,"@type":112},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":118,"interactionType":119,"userInteractionCount":72},"InteractionCounter",{"@type":120},"ViewAction",{"@type":122,"mainEntity":123},"FAQPage",[124,130,134],{"name":125,"@type":126,"acceptedAnswer":127},"What technique is primarily used to solve the problems in this worksheet?","Question",{"text":128,"@type":129},"The worksheet focuses on the method of integration by substitution, where a variable 'u' is used to simplify complex integrals into solvable forms.","Answer",{"name":131,"@type":126,"acceptedAnswer":132},"What types of functions are covered in these integration exercises?",{"text":133,"@type":129},"The problems involve a variety of functions, including polynomial, exponential, natural logarithmic, and trigonometric functions.",{"name":135,"@type":126,"acceptedAnswer":136},"Are the solutions provided for the practice problems?",{"text":137,"@type":129},"Yes, the document provides the evaluated indefinite integrals for both the guided substitution problems and the independent exercises.","https://schema.org",{"og:url":100,"og:type":140,"og:title":65,"og:site_name":111,"og:description":66},"article",{"robots":142,"canonical":100},"index,follow",{"doc_id":61,"site_id":75},1791489405]