{"id":686,"date":"2020-12-04T14:42:36","date_gmt":"2020-12-04T12:42:36","guid":{"rendered":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=686"},"modified":"2020-12-05T11:40:52","modified_gmt":"2020-12-05T09:40:52","slug":"integracion-de-formas-compuestas","status":"publish","type":"post","link":"https:\/\/www.pealfa.duckdns.org\/wordpress\/?p=686","title":{"rendered":"Integraci\u00f3n de formas compuestas"},"content":{"rendered":"<style type=\"text\/css\">\nboton {\n border: none;\n background: rgba(0,0,0,0);\n color: #3a7999;\n box-shadow: inset 0 0 0 3px #3a7999;\n padding: 10px;\n font-size: 125%;\n border-radius: 5px;\n position: relative;\n box-sizing: border-box;\n}\n<\/style>\n<p><script type=\"text\/javascript\">function SINO(cual) {\n   var elElemento=document.getElementById(cual);\n   if(elElemento.style.display == 'block') {\n      elElemento.style.display = 'none';\n   } else {\n      elElemento.style.display = 'block';\n   }\n}\n<\/script><\/p>\n<p>Hola. En la entrada previa a esta nos introducimos en el \u00abC\u00e1lculo de Primitivas\u00bb. Hoy vamos a dar un paso m\u00e1s: estudiaremos las llamadas \u00abintegrales de formas compuestas\u00bb. \u00bfY esto qu\u00e9 es? Pues el intento de calcular la primitiva de una funci\u00f3n deshaciendo la Regla de la Cadena.<\/p>\n<p>Si aplicamos la Regla de la Cadena en sentido inverso obtenemos integrales como la siguiente:<\/p>\n<p>\\[\\int{u'(x)\\cos{u(x)}}\\,{\\rm d}x=\\operatorname{sen}{u(x)}+C\\]<br \/>\nDonde \\(u\\) es una funci\u00f3n derivable.<\/p>\n<p>Ese tipo de integrales es el que aparece en las habituales \u00abtablas de formas compuestas\u00bb y que puedes encontrar en nuestra <sa href=\"https:\/\/www.dropbox.com\/sh\/hvs3wyz9osqxc70\/AADlVprdl7TPNTGvTSDCYk3aa?dl=0\">carpeta de materiales<\/a>, tanto en el texto como en el esquema de la lecci\u00f3n.<\/p>\n<p>Aqu\u00ed tenemos una lista de ellas para practicar:<\/p>\n<fieldset style=\"border: 1px solid #8A0808; padding: 10px;\">\n<div style=\"text-align: center;\">OBTENGAMOS LAS SIGUIENTES PRIMITIVAS<\/div>\n<ol>\n<li>\\( \\displaystyle{\\int\\!{\\rm e}^{\\operatorname{sen}{x}}\\cos{x}\\,\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!x^2 \\cos{x^3}\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{2x+3}{x^2+3x}\\,\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{x^2}{1+\\left(x^3-2\\right)^2}\\,\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{x^3}{x^4+1}\\,\\mathrm{d}x}\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{1}{x}\\operatorname{sen}\\left(\\ln{x}\\right)\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!x\\left(x^2-7\\right)^5\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{3x}{x^4+1}\\,\\mathrm{d}x}\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!\\frac{5}{\\cos^2\\left(3x\\right)}\\,\\mathrm{d}x }\\)<\/li>\n<p><\/p>\n<li>\\( \\displaystyle{\\int\\!x\\left(x^2-7\\right)^5\\mathrm{d}x }\\)<\/li>\n<p>\n<\/fieldset>\n<p>Si no sabes obtenerlas, necesitas ayuda o quieres comprobar, todas se obtienen detenidamente en estos dos v\u00eddeos:<\/p>\n<table width=\"100%\">\n<tbody>\n<tr>\n<th width=\"50%\">Integrales compuestas 1<\/th>\n<th width=\"50%\">Integrales compuestas 2<\/th>\n<\/tr>\n<tr>\n<th width=\"50%\"><iframe src=\"https:\/\/www.youtube.com\/embed\/gXQumyT1_vg?showinfo=0\" 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\/5ZPMquxe9Dc?showinfo=0\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/th>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Aqu\u00ed una sencilla cuesti\u00f3n para ver si hemos comprendido:<\/p>\n<form name=\"ejercicio\">\n<fieldset style=\"border: 1px solid #8A0808; padding: 10px;\">\n<div class=\"pregunta\">\n<div style=\"text-align: center;\">CUESTI\u00d3N<\/div>\n<p>Obtengamos<br \/>\n\\[\\int\\frac{5}{\\sqrt{1-\\left(3x-1\\right)^2}}\\,{\\rm d}x\\]<br \/>\n<\/fieldset>\n<\/form>\n<p><\/p>\n<p>En caso de duda, podemos mostrar \/ ocultar una sugerencia al pulsar sobre &#10067; y una resoluci\u00f3n pulsando sobre <span style=\"color:#FF0000; font-size:110%;\">&#9997;<\/span>.<\/p>\n<table cellpadding=\"5\" cellspacing=\"0\" style=\"border: none; padding: 0cm; width: 100%\">\n<tbody>\n<tr>\n<td width=\"50%\" style=\"border: none;\">\n<div style=\"text-align: center;\">\n<boton><a href=\"javascript:void(0);\" onclick=\"SINO('suger1')\" style=\"text-decoration: none;\" title=\"Ver sugerencia\">&#10067;<\/a><\/boton><\/div>\n<\/td>\n<td width=\"50%\" style=\"border: none;\">\n<div style=\"text-align: center;\"><boton><a href=\"javascript:void(0);\" onclick=\"SINO('solu1')\" style=\"text-decoration: none;\" title=\"Ver soluci\u00f3n\"> &#9997; <\/a><\/boton><\/div>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"suger1\" style=\"display: none;\">\n<hr \/>\n<p>SUGERENCIA:<\/p>\n<p>Observa que es una forma compuesta de tipo arco-seno.<\/p>\n<hr \/>\n<\/div>\n<div id=\"solu1\" style=\"display: none;\">\n<hr \/>\n<p>SOLUCI\u00d3N:<\/p>\n<p>\\[\\int\\frac{5}{\\sqrt{1-\\left(3x-1\\right)^2}}\\,{\\rm d}x=\\frac{5}{3}\\int\\frac{3}{\\sqrt{1-\\left(3x-1\\right)^2}}\\,{\\rm d}x=\\frac{5}{3}\\operatorname{arcsen}\\left(3x-1\\right)+C   \\]<\/p>\n<hr \/>\n<\/div>\n<p>\u00bfHa ido todo bien? Espero que se hayan disipado las dudas con las explicaciones y que hayas finalmente obtenido esas integrales.<\/p>\n<p>Gracias y hasta pronto.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hola. En la entrada previa a esta nos introducimos en el \u00abC\u00e1lculo de Primitivas\u00bb. Hoy vamos a dar un paso m\u00e1s: estudiaremos [&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-686","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\/686","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=686"}],"version-history":[{"count":5,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/686\/revisions"}],"predecessor-version":[{"id":693,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/686\/revisions\/693"}],"wp:attachment":[{"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=686"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=686"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.pealfa.duckdns.org\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=686"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}