[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522904-105":59,"doc-detail-522904-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","integration-by-parts-calculus-practice-worksheet","Integration by Parts - Calculus Practice Worksheet","","This document provides a structured set of calculus practice problems focused on the integration by parts technique. Designed for students and educators, it includes ten specific indefinite integral exercises, with the first four providing suggested u and dv variables to guide the solution process. The second half of the document serves as an answer key or solution guide, detailing the step-by-step mathematical resolutions for each of the ten problems, demonstrating the correct application of the integration by parts formula to various functions involving exponential, logarithmic, and trigonometric components. This resource is suitable for supplemental classroom practice or independent study in an introductory calculus course.",{"@graph":69,"@context":122},[70,84,105],{"@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-parts-calculus-practice-worksheet/522904/",{"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-parts-calculus-practice-worksheet/522904.png","ImageObject",300,407,{"name":92,"@type":93},"วิน","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What technique is used to evaluate the indefinite integrals in this worksheet?","Question",{"text":112,"@type":113},"The worksheet focuses exclusively on the integration by parts technique, which is based on the formula derived from the product rule of differentiation.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Are all problems provided with the substitution variables u and dv?",{"text":117,"@type":113},"No, only the first four problems include suggested u and dv values. The remaining six problems require the student to independently determine the appropriate substitutions to evaluate the integrals.",{"name":119,"@type":110,"acceptedAnswer":120},"Does the document provide solutions to the problems?",{"text":121,"@type":113},"Yes, the document includes an answer key section that provides the final results or detailed steps for all ten problems listed in the exercises.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522904,1791582068,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24,"preview_page_count":4},2336475104736,"https://ap-avatar.wpscdn.com/avatar/22000c4c5e0e5b17e70?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786591360781797222","Kuta Software-Infinite Calculus Name   \nIntegration by Parts Date  Period   \nEvaluate each indefinite integral using integration by parts. u and dv are provided.  \n1) ∫ xex dx; u = x, dv = ex dx 2) ∫ xcos x dx; u = x, dv = cos x dx  \n3) ∫ x ⋅ 2x dx; u = x, dv = 2 x dx 4) ∫ ln x dx; u = ln x , dv =  dx  \nEvaluate each indefinite integral.  \n5) ∫ xe−x dx 6) ∫ x 2 cos 3x dx  \n7) ∫ ~~ ~~xe22x~~ ~~ dx 8) ∫ x 2 e 5x dx  \n9) ∫ ln (x + 3) dx 10) ∫ cos 2x ⋅ e −x dx  \nKuta Software-Infinite Calculus Name   \nIntegration by Parts Date  Period   \nEvaluate each indefinite integral using integration by parts. u and dv are provided.  \n1) ∫ xex dx; u = x, dv = ex dx  \nx x  \nxe − e + C  \n3) ∫ x ⋅ 2x dx; u = x, dv = 2 x dx  \nx ⋅ 2 x  \nln 2  \n−  \n2 x  \n(ln 2)2  \n+ C  \nEvaluate each indefinite integral.  \n5) ∫ xe−x dx  \nUse: u = x, dv = e −x dx ∫ xe−x dx = −x~~ ~~−~~ ~~1~~ ~~ + C  \nex  \n7) ∫ ~~ ~~xe22x~~ ~~ dx  \nUse: u = x2 , dv = ~~ ~~e12x~~ ~~ dx ∫  x 2  dx = −2x2 − 2x − 1  + C  \ne 2x 4e2x  \n9) ∫ ln (x + 3) dx  \nUse: u = ln (x + 3) , dv = dx *or use u-subs first  \n∫  \nln (x + 3) dx = x ln (x + 3) − x + 3 ln (x + 3) + C  \n2) ∫ xcos x dx; u = x, dv = cos x dx  \nxsin x + cos x + C  \n4) ∫ ln x dx; u = ln x , dv =  dx  \n3   3  \n2 2  \n2x~~ ~~ln3~~ ~~x − 4x9~~ ~~ + C  \n6) ∫ x 2 cos 3x dx  \n2  \nUse: u = x , dv = cos 3x dx  \n∫ x cos 3x dx = ~~ ~~ + ~~ ~~ − ~~ ~~ + C  \n2 x2 sin 3x 2xcos 3x 2sin 3x 3 9 27  \n8) ∫ x 2 e 5x dx  \nUse: u = x 2 , dv = e 5x dx  \n2 5x x2 e 5x 2xe5x 2e5x  \n∫ x e dx = ~~ ~~ − ~~ ~~ + ~~ ~~ + C  \n5 25 125  \n10) ∫ cos 2x ⋅ e −x dx  \n−x  \nUse: u = e , dv = cos 2x dx  \n∫ cos 2x ⋅ e −x dx =  2sin 2x − cos 2x + C  \n5ex  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaibp4yegv1qzQ","https://ap.wps.com/l/cbCaibp4yegv1qzQ","pdf",33792,"English","# Integration by Parts Exercises\n## Guided Problems with u and dv\n## Indefinite Integral Evaluations\n# Answer Key and Solutions","[{\"question\":\"What technique is used to evaluate the indefinite integrals in this worksheet?\",\"answer\":\"The worksheet focuses exclusively on the integration by parts technique, which is based on the formula derived from the product rule of differentiation.\"},{\"question\":\"Are all problems provided with the substitution variables u and dv?\",\"answer\":\"No, only the first four problems include suggested u and dv values. The remaining six problems require the student to independently determine the appropriate substitutions to evaluate the integrals.\"},{\"question\":\"Does the document provide solutions to the problems?\",\"answer\":\"Yes, the document includes an answer key section that provides the final results or detailed steps for all ten problems listed in the exercises.\"}]","Integration by Parts - Calculus Practice Worksheet | PDF",1791426292]