{"id":4141,"date":"2025-06-03T18:11:22","date_gmt":"2025-06-03T18:11:22","guid":{"rendered":"https:\/\/lash.utrng.edu.mx\/?p=4141"},"modified":"2025-07-11T01:17:02","modified_gmt":"2025-07-11T01:17:02","slug":"antiderivada-integral-indefinida","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=4141","title":{"rendered":"01. Antiderivada \/ Integral Indefinida"},"content":{"rendered":"<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1024\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/antiderivada-1-1024x1024.jpg\" alt=\"\" class=\"wp-image-4143\" style=\"width:544px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/antiderivada-1-1024x1024.jpg 1024w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/antiderivada-1-300x300.jpg 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/antiderivada-1-150x150.jpg 150w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/antiderivada-1-768x768.jpg 768w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/antiderivada-1-1536x1536.jpg 1536w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/antiderivada-1.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure><\/div>\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-d8ddc7656578ab9799e01a4debf0ff71\">Antiderivadas<\/h3>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-1d81d9856f5589da91c0c02a9096bc1d\">La mayor\u00eda de las operaciones matem\u00e1ticas con que trabajamos vienen en pares de inversas: suma y resta, multiplicaci\u00f3n y divisi\u00f3n, y exponenciaci\u00f3n y extracci\u00f3n de ra\u00edces. Una raz\u00f3n de operaciones inversas es su utilidad en la resoluci\u00f3n de ecuaciones. Por ejemplo, la resoluci\u00f3n de x<sup>3<\/sup> = 8, esto implica el uso de extraer ra\u00edces.<\/p>\n\n\n\n<!--more-->\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-c9c494c93d91a7d0063043e8194034be\">Si queremos resolver ecuaciones que incluyan <strong>derivadas <\/strong>necesitaremos su inversa, denominada <strong>antiderivaci\u00f3n o integraci\u00f3n<\/strong>.<\/p>\n\n\n\n<details class=\"wp-block-details\"><summary><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color is-layout-flow wp-block-details-is-layout-flow\"><strong>Definici\u00f3n<\/strong><\/mark>(click Expandir\/contraer)<\/summary>\n<p>Llamamos a F una <strong>antiderivada <\/strong>de <em>f <\/em>en el intervalo I si D<sub>x<\/sub>F(x) = <em>f<\/em> (x) en I; esto es, si F'(x) = <em>f<\/em> (x) para toda x en I.<\/p>\n<\/details>\n\n\n\n<h3 class=\"wp-block-heading has-vivid-cyan-blue-color has-black-background-color has-text-color has-background has-link-color wp-elements-cb53074ff04fa329399e92f1a87e8857\">Ejemplo<\/h3>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-63c2784481acacbd368c14ab56a00a5e\"><strong>1<\/strong>. Encuentre una antiderivada de la funci\u00f3n <em>f<\/em> (x) = 4x<sup>3<\/sup> en (- <em>\u221e<\/em>,<em>\u221e<\/em>).<\/p>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-40e866c3d9f5893154b284d649334e7a\"><strong>SOLUCI\u00d3N<\/strong>: Buscamos una funci\u00f3n F que satisfaga F'(x) = 4x<sup>3<\/sup> para toda x real.<\/p>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:46% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"307\" height=\"262\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image.png\" alt=\"\" class=\"wp-image-4154 size-full\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image.png 307w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-300x256.png 300w\" sizes=\"auto, (max-width: 307px) 100vw, 307px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p>La funci\u00f3n F(x) = x<sup>4<\/sup> + 6 tambi\u00e9n satisface F'(x) = 4x<sup>3<\/sup>; tambi\u00e9n es una antiderivada de<em> f <\/em>(x) = 4x<sup>3<\/sup>.<br>De hecho, F(x) = x4 + C, donde C es cualquier constante, es una antiderivada de 4x<sup>3 <\/sup>en (- <em>\u221e<\/em>,<em>\u221e<\/em>)<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-1135a4afab435a45f67cf20c6d8cd32a\"><strong>2<\/strong>. Encuentre la antiderivada general de <em>f <\/em>(x) = x<sup>2<\/sup> en (- <em>\u221e<\/em>,<em>\u221e<\/em>).<\/p>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-2cedfdca16144f37b0812c10ba09d0e1\">SOLUCI\u00d3N: la antiderivada general es <img loading=\"lazy\" decoding=\"async\" width=\"104\" height=\"47\" class=\"wp-image-4160\" style=\"width: 104px;\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-1.png\" alt=\"\"><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:44% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"272\" height=\"78\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-2.png\" alt=\"\" class=\"wp-image-4163 size-full\"\/><\/figure><div class=\"wp-block-media-text__content\">\n<p><strong>Regla para la potencia<\/strong>.<\/p>\n\n\n\n<p>Si r es cualquier n\u00famero racional, excepto -1, entonces<\/p>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-84829cac6f86380c1ca62e13faaae956\">Siguiendo a Leibniz, a veces usaremos el t\u00e9rmino <strong>integral indefinida<\/strong> en lugar de<br><strong>antiderivada<\/strong>. <strong>Antiderivar <\/strong>tambi\u00e9n es <strong>integrar<\/strong>. En el s\u00edmbolo <img loading=\"lazy\" decoding=\"async\" width=\"128\" height=\"28\" class=\"wp-image-4166\" style=\"width: 128px;\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-3.png\" alt=\"\"> se denomina <strong>signo de integral<\/strong> y <em>f<\/em> (x) se llama <strong>integrando<\/strong>.<\/p>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-bb4dd0c031043cbba088d425009953e4\"><strong>3.<\/strong> Encuentre la antiderivada general de <img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"42\" class=\"wp-image-4170\" style=\"width: 100px;\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-5.png\" alt=\"\"><\/p>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-4d8d6009019f32e28fd47f518c8b4e5a\">SOLUCI\u00d3N:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"316\" height=\"64\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-6.png\" alt=\"\" class=\"wp-image-4172\" style=\"width:336px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-6.png 316w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-6-300x61.png 300w\" sizes=\"auto, (max-width: 316px) 100vw, 316px\" \/><\/figure><\/div>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:45% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"240\" height=\"58\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-7.png\" alt=\"\" class=\"wp-image-4174 size-full\"\/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-text-align-center\"><strong>Regla para la Sen y Cos<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:45% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"221\" height=\"62\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-8.png\" alt=\"\" class=\"wp-image-4175 size-full\"\/><\/figure><div class=\"wp-block-media-text__content\">\n<p>Las f\u00f3rmulas de antiderivadas para las funciones seno y coseno se deducen directamente de la derivada<\/p>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-05632029db11419b895fe2527d27a9af\"><\/p>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"439\" height=\"177\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-9.png\" alt=\"\" class=\"wp-image-4177 size-full\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-9.png 439w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-9-300x121.png 300w\" sizes=\"auto, (max-width: 439px) 100vw, 439px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p><strong>La integral indefinida es un operador lineal<\/strong>.<\/p>\n\n\n\n<p>Suponga que f y g tienen antiderivadas (integrales indefinidas) y sea k una constante. Entonces:<\/p>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-ebe5eea7e68ab1ab14bc187444099dd0\"><strong>4.<\/strong> Mediante la linealidad de <img loading=\"lazy\" decoding=\"async\" width=\"29\" height=\"31\" class=\"wp-image-4180\" style=\"width: 29px;\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-10.png\" alt=\"\"> eval\u00fae:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"710\" height=\"62\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-11.png\" alt=\"\" class=\"wp-image-4181\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-11.png 710w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-11-300x26.png 300w\" sizes=\"auto, (max-width: 710px) 100vw, 710px\" \/><\/figure>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-4d8d6009019f32e28fd47f518c8b4e5a\">SOLUCI\u00d3N:<\/p>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-05632029db11419b895fe2527d27a9af\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"574\" height=\"251\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-12.png\" alt=\"\" class=\"wp-image-4182\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-12.png 574w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-12-300x131.png 300w\" sizes=\"auto, (max-width: 574px) 100vw, 574px\" \/><\/figure>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-ee842d34a439e363238c12c807d7c1a0\">Aparecieron dos constantes arbitrarias C1 y C2, pero se combinaron en una constante, C<\/p>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-be3920ffd9cdb6717f0c6a221cff7d94\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-black-color\">(b)<\/mark>. Observe el uso de la variable <strong>u<\/strong> en lugar de <strong>x<\/strong>. Esto est\u00e1 bien mientras que el correspondiente s\u00edmbolo de la diferencial sea <strong>du<\/strong>; entonces, tenemos un cambio completo en la notaci\u00f3n.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"539\" height=\"96\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-13.png\" alt=\"\" class=\"wp-image-4183\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-13.png 539w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-13-300x53.png 300w\" sizes=\"auto, (max-width: 539px) 100vw, 539px\" \/><\/figure><\/div>\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"627\" height=\"126\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-14.png\" alt=\"\" class=\"wp-image-4184\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-14.png 627w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-14-300x60.png 300w\" sizes=\"auto, (max-width: 627px) 100vw, 627px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<div class=\"wp-block-media-text is-stacked-on-mobile\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"322\" height=\"66\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-15.png\" alt=\"\" class=\"wp-image-4187 size-full\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-15.png 322w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-15-300x61.png 300w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p><strong>Regla generalizada de la potencia<\/strong><\/p>\n\n\n\n<p>Sean <strong><em>g<\/em><\/strong> una funci\u00f3n derivable y <em><strong>r <\/strong><\/em>un n\u00famero racional diferente de -1. Entonces<\/p>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-a4d9996a2ea25cbeb73797e204973acf\"><strong>5. <\/strong>Evalue:<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"553\" height=\"58\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-16.png\" alt=\"\" class=\"wp-image-4189\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-16.png 553w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-16-300x31.png 300w\" sizes=\"auto, (max-width: 553px) 100vw, 553px\" \/><\/figure><\/div>\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-4d8d6009019f32e28fd47f518c8b4e5a\">SOLUCI\u00d3N:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"654\" height=\"172\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-18.png\" alt=\"\" class=\"wp-image-4190\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-18.png 654w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-18-300x79.png 300w\" sizes=\"auto, (max-width: 654px) 100vw, 654px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"615\" height=\"162\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-19.png\" alt=\"\" class=\"wp-image-4191\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-19.png 615w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-19-300x79.png 300w\" sizes=\"auto, (max-width: 615px) 100vw, 615px\" \/><\/figure>\n\n\n\n<p class=\"has-vivid-cyan-blue-color has-text-color has-link-color wp-elements-14a9f015cb228bb918513ae9a933494f\">En este ejemplo(a), Leibniz us\u00f3 la diferencial <strong>dx<\/strong> en su notaci\u00f3n <img loading=\"lazy\" decoding=\"async\" width=\"29\" height=\"31\" class=\"wp-image-4180\" style=\"width: 29px;\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-10.png\" alt=\"\">&#8230;dx Si hacemos u=g(x), entonces du = g'(x)dx.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-white-color has-black-background-color has-text-color has-background has-link-color wp-elements-14938e4e883afa429fcbd76b0b169e67\">Ejercicios<\/h3>\n\n\n\n<p>Encontrar la antiderivada general de los siguientes ejercicios y envia al correo siguiente: <strong>lsaucedoh@utrng.edu.mx<\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"424\" height=\"158\" src=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-20.png\" alt=\"\" class=\"wp-image-4196\" style=\"width:568px;height:auto\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-20.png 424w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2025\/06\/image-20-300x112.png 300w\" sizes=\"auto, (max-width: 424px) 100vw, 424px\" \/><\/figure><\/div>\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Antiderivadas La mayor\u00eda de las operaciones matem\u00e1ticas con que trabajamos vienen en pares de inversas: suma y resta, multiplicaci\u00f3n y divisi\u00f3n, y exponenciaci\u00f3n y extracci\u00f3n de ra\u00edces. Una raz\u00f3n de operaciones inversas es su utilidad en la resoluci\u00f3n de ecuaciones. Por ejemplo, la resoluci\u00f3n de x3 = 8, esto implica el uso de extraer ra\u00edces.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[99],"tags":[],"class_list":["post-4141","post","type-post","status-publish","format-standard","hentry","category-calcintegral-primparc"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/4141","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4141"}],"version-history":[{"count":20,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/4141\/revisions"}],"predecessor-version":[{"id":4223,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/4141\/revisions\/4223"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}