{"id":707,"date":"2020-12-09T14:46:01","date_gmt":"2020-12-09T12:46:01","guid":{"rendered":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=707"},"modified":"2020-12-09T14:46:01","modified_gmt":"2020-12-09T12:46:01","slug":"integracion-de-funciones-racionales-i","status":"publish","type":"post","link":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=707","title":{"rendered":"Integraci\u00f3n de funciones racionales (I)"},"content":{"rendered":"<p>Buenas. \u00bfC\u00f3mo van esas integrales? \u00bfPreparados para m\u00e1s?<\/p>\n<p>Hoy vamos a dedicar esta entrada a las integrales de las funciones racionales, esto es, de fracciones de polinomios. Vamos a obtener primitivas de tales funciones, pero s\u00f3lo de los casos m\u00e1s sencillos.<\/p>\n<p>Concretamente, vamos a obtener las siguientes:<\/p>\n<fieldset style=\"border: 1px solid #8A0808; padding: 10px;\">\n<div style=\"text-align: center;\">INTEGRALES<\/div>\n<ol>\n<li>\\( \\displaystyle{\\int\\! \\frac{4}{2x+1}\\,\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{4}{x^2+1}\\,\\,\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{4x^2}{2x+1}\\,\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{4x^2}{x^2+1}\\,\\,\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{8x-7}{x^2-x-2}\\,\\,\\mathrm{d}x }\\)<\/li>\n<p>\n<\/fieldset>\n<p>Las dos primeras son inmediatas, las dos siguientes se convierten en inmediatas efectuando la divisi\u00f3n entera y la \u00faltima se obtiene por descomposici\u00f3n en fracciones simples. \u00bfQue no sabes de qu\u00e9 hablamos? Pues en los v\u00eddeos siguientes est\u00e1 bien explicadito y, aunque conozcas el proceder m\u00e1s conveniente, te vendr\u00e1 bien para repasar. La \u00faltima es exclusiva del segundo v\u00eddeo:<\/p>\n<table width=\"100%\">\n<tbody>\n<tr>\n<th width=\"50%\">Integrales racionales 1<\/th>\n<th width=\"50%\">Integrales racionales 2<\/th>\n<\/tr>\n<tr>\n<th width=\"50%\"><iframe src=\"https:\/\/www.youtube.com\/embed\/6BzYFD4ihTQ\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/th>\n<th width=\"50%\"><iframe src=\"https:\/\/www.youtube.com\/embed\/7x2xA_0bGLE\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/th>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Espero que todo est\u00e9 bien expuesto y haya sido \u00fatil.<\/p>\n<p>Gracias por tu visita y hasta la siguiente.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Buenas. \u00bfC\u00f3mo van esas integrales? \u00bfPreparados para m\u00e1s? Hoy vamos a dedicar esta entrada a las integrales de las funciones racionales, esto [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"post-templates\/post_nosidebar.php","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[61,60,50],"class_list":["post-707","post","type-post","status-publish","format-standard","hentry","category-matematicas-ii","tag-calculo-integral","tag-integrales-indefinidas","tag-video"],"_links":{"self":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/707","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=707"}],"version-history":[{"count":1,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/707\/revisions"}],"predecessor-version":[{"id":708,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/707\/revisions\/708"}],"wp:attachment":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=707"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=707"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=707"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}