{"id":487,"date":"2025-02-13T19:45:24","date_gmt":"2025-02-13T19:45:24","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/integrals-exponential-functions-and-logarithms-apply-it\/"},"modified":"2025-02-13T19:45:24","modified_gmt":"2025-02-13T19:45:24","slug":"integrals-exponential-functions-and-logarithms-apply-it","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/calculus2\/chapter\/integrals-exponential-functions-and-logarithms-apply-it\/","title":{"raw":"Integrals, Exponential Functions, and Logarithms: Apply It","rendered":"Integrals, Exponential Functions, and Logarithms: Apply It"},"content":{"raw":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Understand the natural logarithm and the mathematical constant [latex]e[\/latex] using integrals<\/li>\n\t<li>Identify how to differentiate the natural logarithm function<\/li>\n\t<li>Perform integrations where the natural logarithm is involved<\/li>\n\t<li>Understand how to find derivatives and integrals of exponential functions<\/li>\n\t<li>Convert logarithmic and exponential expressions to base e forms<\/li>\n<\/ul>\n<\/section>\n<h2>Integrals, Exponential Functions, and Logarithms<\/h2>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/zmnh448y_ZU?si=xK_q41S_THs-JGGl\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/section>\n","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Understand the natural logarithm and the mathematical constant [latex]e[\/latex] using integrals<\/li>\n<li>Identify how to differentiate the natural logarithm function<\/li>\n<li>Perform integrations where the natural logarithm is involved<\/li>\n<li>Understand how to find derivatives and integrals of exponential functions<\/li>\n<li>Convert logarithmic and exponential expressions to base e forms<\/li>\n<\/ul>\n<\/section>\n<h2>Integrals, Exponential Functions, and Logarithms<\/h2>\n<section class=\"textbox watchIt\" aria-label=\"Watch It\">\n<iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/zmnh448y_ZU?si=xK_q41S_THs-JGGl\" title=\"YouTube video player\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><br \/>\n<\/section>\n","protected":false},"author":6,"menu_order":8,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":479,"module-header":"","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/487"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/487\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/parts\/479"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapters\/487\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/media?parent=487"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/pressbooks\/v2\/chapter-type?post=487"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/contributor?post=487"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/calculus2\/wp-json\/wp\/v2\/license?post=487"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}