{"id":21455,"date":"2025-08-18T23:42:58","date_gmt":"2025-08-18T15:42:58","guid":{"rendered":"https:\/\/blog.iyatt.com\/?p=21455"},"modified":"2025-08-22T10:09:16","modified_gmt":"2025-08-22T02:09:16","slug":"csc-x-%e7%9a%84%e4%b8%8d%e5%ae%9a%e7%a7%af%e5%88%86%e8%ae%a1%e7%ae%97","status":"publish","type":"post","link":"https:\/\/blog.iyatt.com\/?p=21455","title":{"rendered":"csc x \u4f59\u5272\u7684\u4e0d\u5b9a\u79ef\u5206\u8ba1\u7b97"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">\u76ee\u5f55<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/blog.iyatt.com\/?p=21455\/#%E5%BD%A2%E5%BC%8F%E4%B8%80\" >\u5f62\u5f0f\u4e00<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/blog.iyatt.com\/?p=21455\/#%E5%BD%A2%E5%BC%8F%E4%BA%8C\" >\u5f62\u5f0f\u4e8c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/blog.iyatt.com\/?p=21455\/#%E5%BD%A2%E5%BC%8F%E4%B8%89\" >\u5f62\u5f0f\u4e09<\/a><\/li><\/ul><\/nav><\/div>\n<h1><span class=\"ez-toc-section\" id=\"%E5%BD%A2%E5%BC%8F%E4%B8%80\"><\/span>\u5f62\u5f0f\u4e00<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<pre><code class=\"language-katex\">\\begin{aligned}\n\\int\\csc\\ x\\ dx&amp;=\\int\\frac1{\\sin x}dx\\\\\n&amp;\\xlongequal{\u4e8c\u500d\u89d2\u516c\u5f0f}\\int\\frac1{2\\sin\\frac{x}2\\cos\\frac{x}2}dx\\\\\n&amp;\\xlongequal{u=\\frac{x}2}\\int\\frac1{\\sin u\\cos u} du\\\\\n&amp;\\xlongequal{\\sin u=\\tan u\\cos u}\\int\\frac1{\\cos^2u\\tan u}du\\\\\n&amp;\\xlongequal{d(\\tan u)=\\sec^2u=\\frac1{\\cos^2u}}\\int\\frac1{\\tan u}d\\tan u\\\\\n&amp;=\\ln|\\tan u|+C\\\\\n&amp;=\\ln|\\tan\\frac{x}2|+C\n\\end{aligned}<\/code><\/pre>\n<h1><span class=\"ez-toc-section\" id=\"%E5%BD%A2%E5%BC%8F%E4%BA%8C\"><\/span>\u5f62\u5f0f\u4e8c<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<p>\u88c2\u9879\u53c2\u8003\uff1a<a href=\"https:\/\/blog.iyatt.com\/?p=20837\">https:\/\/blog.iyatt.com\/?p=20837<\/a><\/p>\n<pre><code class=\"language-katex\">\\begin{aligned}\n\\int\\csc\\ x\\ dx&amp;=\\int\\frac1{\\sin x}dx\\\\\n&amp;=\\int\\frac{\\sin x}{\\sin^2x}dx\\\\\n&amp;\\xlongequal{d\\cos x=-\\sin x}-\\int\\frac1{\\sin^2x}d\\cos x\\\\\n&amp;\\xlongequal{\\sin^2x+\\cos^2x=1}\\int\\frac1{\\cos^2x-1}d\\cos x\\\\\n&amp;=\\int\\frac1{(\\cos x+1)(\\cos x-1)}d\\cos x\\\\\n&amp;\\xlongequal{\u88c2\u9879}\\frac12\\int(\\frac1{\\cos x-1}-\\frac1{\\cos x+1})d\\cos x\\\\\n&amp;=\\frac12(\\ln|\\cos x - 1|)-\\ln(\\cos x+1)+C\\\\\n&amp;=\\frac12\\ln|\\frac{\\cos x-1}{\\cos x+1}|+C\n\n\\end{aligned}<\/code><\/pre>\n<h1><span class=\"ez-toc-section\" id=\"%E5%BD%A2%E5%BC%8F%E4%B8%89\"><\/span>\u5f62\u5f0f\u4e09<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<pre><code class=\"language-katex\">\\begin{aligned}\n\\int\\csc x dx&amp;=\\int\\csc x\\frac{\\csc x-\\cot x}{\\csc x-\\cot x}dx\\\\\n&amp;=\\int\\frac{\\csc^2x-\\csc x\\cot x}{\\csc x-\\cot x}dx\\\\\n&amp;\\xlongequal[du=-\\csc x\\cot x+\\csc^2x]{u=\\csc x-\\cot x}\\int\\frac1{u}du\\\\\n&amp;=\\ln|u|+C\\\\\n&amp;=\\ln|\\csc x-\\cot x|+C &lt;----\u8fd9\u662f\u4e00\u79cd\u7ed3\u679c \\\\\n&amp;\\xlongequal[\\csc x-\\cot x=\\frac1{\\csc x+\\cot x}]{\\csc^2x-\\cot^2x=1}\\ln|(\\csc x+\\cot x)^{-1}|+C\\\\\n&amp;=-\\ln|\\csc x+\\cot x|+C &lt;----\u8fd9\u662f\u53e6\u5916\u4e00\u79cd\u7ed3\u679c\n\\end{aligned}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u5f62\u5f0f\u4e00 \\begin{aligned} \\int\\csc\\ x\\ dx&amp;=\\int\\frac1{\\si [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"zakra_page_container_layout":"customizer","zakra_page_sidebar_layout":"customizer","zakra_remove_content_margin":false,"zakra_sidebar":"customizer","zakra_transparent_header":"customizer","zakra_logo":0,"zakra_main_header_style":"default","zakra_menu_item_color":"","zakra_menu_item_hover_color":"","zakra_menu_item_active_color":"","zakra_menu_active_style":"","zakra_page_header":true,"_lmt_disableupdate":"no","_lmt_disable":"no","footnotes":""},"categories":[1,612],"tags":[1039,1038,1040,1042,1037,655,1047,1045,1043,1046,1044,1041,907],"class_list":["post-21455","post","type-post","status-publish","format-standard","hentry","category-all","category-612","tag-csc-x","tag-1038","tag-1040","tag-1042","tag-1037","tag-655","tag-1047","tag-1045","tag-1043","tag-1046","tag-1044","tag-1041","tag-907"],"modified_by":"IYATT-yx","_links":{"self":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21455","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=21455"}],"version-history":[{"count":8,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21455\/revisions"}],"predecessor-version":[{"id":21475,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=\/wp\/v2\/posts\/21455\/revisions\/21475"}],"wp:attachment":[{"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=21455"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=21455"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.iyatt.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=21455"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}