[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-522891-en":3,"doc-seo-522891-105":30,"detail-sidebar-cat-0-en-105":97},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":11,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29,"preview_page_count":4},522891,549768702563,"Fahsai","https://ap-avatar.wpscdn.com/avatar/8000c4aa63b76e948b?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786536092046926083",4,"Exam","Integration by Substitution - Part 5 - Evaluate Each Indefinite Integral","Worksheets on integration by substitution provide guided practice for evaluating indefinite integrals. The problems require using a given substitution variable u to simplify each integrand, then expressing the result in terms of u and converting back to x. The set covers multiple forms, including powers of polynomials, expressions involving logarithms, trigonometric functions with sec and tan, and exponential terms, each ending with an arbitrary constant C.","Kuta Software-Infinite Calculus Name___________________________________  \nIntegration by Substitution Date________________ Period____  \nEvaluate each indefinite integral. Use the provided substitution.  \n1) ∫ −15x4 (−3x5 − 1) 5 dx; u = −3x5 − 1 2) ∫ −16x3 (−4x4 − 1)−5 dx; u = −4x4 − 1  \n3) ∫ − ~~ ~~(−28x4x~~ ~~5)~~ ~~5~~ ~~ dx; u = −2x4 + 5 4) ∫ (5x4 + 5) ~~ ~~23 ⋅ 20x3 dx; u = 5x4 + 5  \n5) ∫ ~~ ~~(5~~ ~~+~~ ~~lnx~~ ~~x~~ ~~)~~ ~~5 dx; u = 5 + ln x 6) ∫ 4sec 4x ⋅ tan 4x ⋅ sec 4 4x dx; u = sec 4x  \n7) ∫ 36x3 (3x4 + 3) 5 dx; u = 3x4 + 3 8) ∫ x(4x − 1)4 dx; u = 4x − 1  \nEvaluate each indefinite integral.  \n9) ∫ −9x2 (−3x3 + 1) 3 dx 10) ∫ 12x3 (3x4 + 4)4 dx  \n11) ∫ −12x2 (−4x3 + 2)−3 dx 12) ∫ (3x5 − 3) ~~ ~~35 ⋅ 15x4 dx  \n13) ∫ (−2x4 − 4)4 ⋅ −32x3 dx 14) ∫ (e 4x − 4)~~ ~~15 ⋅ 8e4x dx  \n15) ∫ x(4x + 5) 3 dx 16) ∫ 5x dx  \nKuta Software-Infinite Calculus Name   \nIntegration by Substitution Date  Period   \nEvaluate each indefinite integral. Use the provided substitution.  \n1) ∫ −15x4 (−3x5 − 1) 5 dx; u = −3x5 − 1  \n16(−3x5 − 1) 6 + C  \n3) ∫ − ~~ ~~(−28x4x~~ ~~5)~~ ~~5~~ ~~ dx; u = −2x4 + 5 1  \n− ~~ ~~ + C 4(−2x4 + 5)4  \n5) ∫ ~~ ~~(5~~ ~~+~~ ~~lnx~~ ~~x~~ ~~)~~ ~~5 dx; u = 5 + ln x  \n16(5 + ln x) 6 + C  \n7) ∫ 36x3 (3x4 + 3) 5 dx; u = 3x4 + 3  \n12(3x4 + 3) 6 + C  \n2) ∫ −16x3 (−4x4 − 1)−5 dx; u = −4x4 − 1 1  \n− ~~ ~~ + C 4(−4x4 − 1)4  \n4) ∫ (5x4 + 5) ~~ ~~23 ⋅ 20x3 dx; u = 5x4 + 5  \n5  \n35(5x4 + 5) 3 + C  \n6) ∫ 4sec 4x ⋅ tan 4x ⋅ sec 4 4x dx; u = sec 4x  \n15 ⋅ sec 5 4x + C  \n8) ∫ x(4x − 1)4 dx; u = 4x − 1  \n916~~ ~~ (4x − 1) 6 + ~~ ~~180(4x − 1) 5 + C  \nEvaluate each indefinite integral.  \n9) ∫ −9x2 (−3x3 + 1) 3 dx  \n14(−3x3 + 1)4 + C  \n11) ∫ −12x2 (−4x3 + 2)−3 dx 1  \n− ~~ ~~ + C 2(−4x3 + 2)2  \n13) ∫ (−2x4 − 4)4 ⋅ −32x3 dx  \n45(−2x4 − 4) 5 + C  \n15) ∫ x(4x + 5) 3 dx  \n180(4x + 5) 5 − ~~ ~~564(4x + 5)4 + C  \n10) ∫ 12x3 (3x4 + 4)4 dx  \n15(3x4 + 4) 5 + C  \n12) ∫ (3x5 − 3) ~~ ~~35 ⋅ 15x4 dx  \n8  \n58(3x5 − 3) 5 + C  \n16) ∫ 5x dx  \n5 3  \n1  2  5  2  \n2  (2x + 3) −  2  (2x + 3) + C  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaidZloPA93C5I","https://ap.wps.com/l/cbCaidZloPA93C5I","pdf",40054,9,1,"English","en",105,"# Evaluate each indefinite integral\n## Use the provided substitution","[{\"question\":\"What does the worksheet ask you to do for each problem?\",\"answer\":\"Evaluate each indefinite integral using the provided substitution.\"},{\"question\":\"How is the substitution variable u used in these exercises?\",\"answer\":\"Each problem gives u in terms of x; you rewrite the integral in terms of u to simplify and then substitute back.\"},{\"question\":\"Do the problems include different types of integrands?\",\"answer\":\"Yes. The worksheet includes polynomial powers, logarithms, trigonometric functions (like sec and tan), and exponential expressions.\"}]","Integration by Substitution - Part 5 - Evaluate Each Indefinite Integral | PDF",1791426280,10,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":91,"head_meta":93,"extra_data":95,"updated_unix":96},"integration-by-substitution-part-5-evaluate-each-indefinite-integral","",{"@graph":36,"@context":90},[37,53,73],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/exam/",3,{"item":52,"name":13,"@type":43,"position":11},"https://docshare.wps.com/document/integration-by-substitution-part-5-evaluate-each-indefinite-integral/522891/",{"url":52,"name":13,"@type":54,"image":55,"author":60,"headline":13,"publisher":62,"fileFormat":65,"inLanguage":23,"description":14,"dateModified":66,"datePublished":67,"encodingFormat":65,"isAccessibleForFree":68,"interactionStatistic":69},"DigitalDocument",{"url":56,"@type":57,"width":58,"height":59},"https://docshare.wps.com/thumbnails/integration-by-substitution-part-5-evaluate-each-indefinite-integral/522891.png","ImageObject",300,407,{"name":9,"@type":61},"Person",{"url":41,"name":63,"@type":64},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":70,"interactionType":71,"userInteractionCount":20},"InteractionCounter",{"@type":72},"ViewAction",{"@type":74,"mainEntity":75},"FAQPage",[76,82,86],{"name":77,"@type":78,"acceptedAnswer":79},"What does the worksheet ask you to do for each problem?","Question",{"text":80,"@type":81},"Evaluate each indefinite integral using the provided substitution.","Answer",{"name":83,"@type":78,"acceptedAnswer":84},"How is the substitution variable u used in these exercises?",{"text":85,"@type":81},"Each problem gives u in terms of x; you rewrite the integral in terms of u to simplify and then substitute back.",{"name":87,"@type":78,"acceptedAnswer":88},"Do the problems include different types of integrands?",{"text":89,"@type":81},"Yes. 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