{"id":33432,"date":"2023-04-04T13:00:41","date_gmt":"2023-04-04T13:00:41","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33432"},"modified":"2025-07-23T10:34:40","modified_gmt":"2025-07-23T10:34:40","slug":"%e4%b8%8d%e5%ae%9a%e7%a9%8d%e5%88%86%e3%81%a8%e5%9f%ba%e6%9c%ac%e7%9a%84%e3%81%aa%e7%a9%8d%e5%88%86%e6%8a%80%e6%b3%95","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ja\/%e4%b8%8d%e5%ae%9a%e7%a9%8d%e5%88%86%e3%81%a8%e5%9f%ba%e6%9c%ac%e7%9a%84%e3%81%aa%e7%a9%8d%e5%88%86%e6%8a%80%e6%b3%95\/","title":{"rendered":"\u4e0d\u5b9a\u7a4d\u5206\u3068\u57fa\u672c\u7684\u306a\u7a4d\u5206\u6280\u6cd5"},"content":{"rendered":"<style>\np, ul, ol {\n    text-align: justify;\n}\nh1, h2, h3 {\ntext-align:center;\n}\n<\/style>\n<p><center><\/p>\n<h1>\u4e0d\u5b9a\u7a4d\u5206\u3068\u57fa\u672c\u7684\u306a\u7a4d\u5206\u6280\u6cd5<\/h1>\n<p><\/center><\/p>\n<p style=\"text-align:center;\">\u3053\u306e\u8b1b\u7fa9\u3067\u306f\u3001\u6700\u3082\u57fa\u672c\u7684\u306a\u4e0d\u5b9a\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u57fa\u672c\u7684\u306a\u6280\u6cd5\u3001\u304a\u3088\u3073\u7a4d\u5206\u6f14\u7b97\u5b50\u306e\u6027\u8cea\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u306f\u3001\u591a\u9805\u5f0f\u3001\u6307\u6570\u95a2\u6570\u3001\u53cc\u66f2\u7dda\u95a2\u6570\u3001\u4e09\u89d2\u95a2\u6570\u306e\u57fa\u672c\u7684\u306a\u7a4d\u5206\u304c\u542b\u307e\u308c\u307e\u3059\u3002<\/em><\/p>\n<p style=\"text-align:center;\"><strong><u>\u5b66\u7fd2\u76ee\u6a19<\/u>:<\/strong><br \/>\u3053\u306e\u8b1b\u7fa9\u306e\u7d42\u4e86\u6642\u306b\u306f\u3001\u5b66\u751f\u306f\u4ee5\u4e0b\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ol>\n<li><strong>\u7406\u89e3\u3059\u308b<\/strong>\uff1a\u4e0d\u5b9a\u7a4d\u5206\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u5fae\u5206\u306e\u9006\u904e\u7a0b\u3068\u3057\u3066\u7406\u89e3\u3059\u308b\u3002<\/li>\n<li><strong>\u8a08\u7b97\u3059\u308b<\/strong>\uff1a\u591a\u9805\u5f0f\u3084\u6307\u6570\u95a2\u6570\u3001\u53cc\u66f2\u7dda\u95a2\u6570\u3001\u4e09\u89d2\u95a2\u6570\u3092\u542b\u3080\u5f0f\u306e\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u3002<\/li>\n<li><strong>\u6d3b\u7528\u3059\u308b<\/strong>\uff1a\u7a4d\u5206\u306e\u6027\u8cea\u3092\u7528\u3044\u3066\u3001\u8a08\u7b97\u3092\u5bb9\u6613\u306b\u3059\u308b\u4ee3\u6570\u7684\u64cd\u4f5c\u3092\u884c\u3046\u3002<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u76ee\u6b21<\/strong><br \/>\n<a href=\"#1\">\u4e0d\u5b9a\u7a4d\u5206\u306e\u91cd\u8981\u6027<\/a><br \/>\n<a href=\"#2\">\u9006\u5fae\u5206\u3001\u4e0d\u5b9a\u7a4d\u5206\u3001\u95a2\u6570\u306e\u539f\u59cb\u95a2\u6570<\/a><br \/>\n<a href=\"#3\">\u57fa\u672c\u7684\u306a\u7a4d\u5206\u6280\u6cd5<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/4wSTxA7zY9k\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u4e0d\u5b9a\u7a4d\u5206\u306e\u91cd\u8981\u6027<\/h2>\n<p>\u4e0d\u5b9a\u7a4d\u5206\u306f\u3001\u5fae\u7a4d\u5206\u306b\u304a\u3044\u3066\u57fa\u672c\u7684\u306a\u9053\u5177\u3067\u3042\u308a\u3001\u7269\u7406\u5b66\u3084\u6570\u5b66\u306b\u304a\u3051\u308b\u5e45\u5e83\u3044\u5fdc\u7528\u304c\u3042\u308a\u307e\u3059\u3002\u4e0e\u3048\u3089\u308c\u305f\u95a2\u6570\u306e\u539f\u59cb\u95a2\u6570\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u3053\u308c\u306f\u66f2\u7dda\u4e0b\u306e\u9762\u7a4d\u3001\u7acb\u4f53\u306e\u4f53\u7a4d\u3001\u78ba\u7387\u306e\u8a08\u7b97\u3001\u3055\u3089\u306b\u306f\u7269\u7406\u5b66\u3001\u5de5\u5b66\u3001\u7d71\u8a08\u5b66\u3001\u7d4c\u6e08\u5b66\u306a\u3069\u306b\u304a\u3051\u308b\u591a\u304f\u306e\u5fdc\u7528\u306b\u7528\u3044\u3089\u308c\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u4e0d\u5b9a\u7a4d\u5206\u306f\u5fae\u5206\u65b9\u7a0b\u5f0f\u306e\u89e3\u6cd5\u306b\u3082\u4e0d\u53ef\u6b20\u3067\u3042\u308a\u3001\u591a\u304f\u306e\u79d1\u5b66\u6280\u8853\u5206\u91ce\u306b\u304a\u3044\u3066\u4e0d\u53ef\u6b20\u306a\u5b58\u5728\u3067\u3059\u3002<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/56fMLiVPwDI\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/center><br \/>\n<a name=\"2\"><\/a><\/p>\n<h2>\u9006\u5fae\u5206\u3001\u4e0d\u5b9a\u7a4d\u5206\u3001\u304a\u3088\u3073\u95a2\u6570\u306e\u539f\u59cb\u95a2\u6570<\/h2>\n<p>\u3042\u308b\u95a2\u6570 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x)<\/span><\/span> \u304c\u3001\u3042\u308b\u533a\u9593 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u306b\u304a\u3044\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u306e\u5c0e\u95a2\u6570\u3067\u3042\u308b\u3068\u304d\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x)<\/span><\/span> \u306f\u305d\u306e\u533a\u9593\u306b\u304a\u3051\u308b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u306e\u539f\u59cb\u95a2\u6570\u3067\u3042\u308b\u3068\u8a00\u3044\u307e\u3059\u3002<\/p>\n<p>\u91cd\u8981\u306a\u306e\u306f\u3001<span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x)<\/span><\/span> \u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u306e\u539f\u59cb\u95a2\u6570\u3067\u3042\u308b\u306a\u3089\u3070\u3001\u4efb\u610f\u306e\u5b9f\u5b9a\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u306b\u5bfe\u3057\u3066 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">F(x) + C<\/span><\/span> \u3082\u307e\u305f <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u306e\u539f\u59cb\u95a2\u6570\u3067\u3042\u308b\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int f(x) dx = F(x) + C<\/span>\n<p>\u5b9a\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u306f<strong>\u7a4d\u5206\u5b9a\u6570<\/strong>\u3068\u547c\u3070\u308c\u3001\u95a2\u6570\u306e\u539f\u59cb\u95a2\u6570\u304c\u4e00\u3064\u306e\u95a2\u6570\u3067\u306f\u306a\u304f\u3001\u5c0e\u95a2\u6570\u304c <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span><\/span> \u3068\u306a\u308b\u3059\u3079\u3066\u306e\u95a2\u6570\u306e\u65cf\u3001\u3059\u306a\u308f\u3061\u95a2\u6570\u306e\u96c6\u5408\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>\n<p>\u300c\u9006\u5fae\u5206\u300d\u300c\u539f\u59cb\u95a2\u6570\u300d\u300c\u4e0d\u5b9a\u7a4d\u5206\u300d\u3068\u3044\u3046\u8a00\u8449\u306f\u3001\u672c\u8cea\u7684\u306b\u540c\u3058\u6982\u5ff5\u3092\u8868\u3057\u3066\u304a\u308a\u3001\u901a\u5e38\u306f\u533a\u5225\u305b\u305a\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u8981\u3059\u308b\u306b\u3001\u4e0d\u5b9a\u7a4d\u5206\u3068\u306f\u5c0e\u95a2\u6570\u306e\u8a08\u7b97\u306b\u5bfe\u3059\u308b\u9006\u306e\u64cd\u4f5c\u3067\u3042\u308a\u3001\u3053\u306e\u767a\u60f3\u304b\u3089\u6700\u3082\u57fa\u672c\u7684\u306a\u6027\u8cea\u304c\u5c0e\u304b\u308c\u307e\u3059\u3002<\/p>\n<h3>\u4e0d\u5b9a\u7a4d\u5206\u306e\u57fa\u672c\u7684\u6027\u8cea<\/h3>\n<p>\u4e0d\u5b9a\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u306b\u306f\u3001\u307e\u305a\u3044\u304f\u3064\u304b\u306e\u57fa\u672c\u7684\u306a\u6027\u8cea\u3092\u77e5\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6027\u8cea\u306f\u3001\u5c0e\u95a2\u6570\u306e\u6027\u8cea\u304b\u3089\u76f4\u63a5\u5f15\u304d\u7d99\u304c\u308c\u305f\u3082\u306e\u3067\u3059\u3002<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int  \\dfrac{df(x)}{dx} dx = f(x) + C<\/span><\/span><\/br>\u4e0d\u5b9a\u7a4d\u5206\u306f\u5fae\u5206\u306e\u9006\u64cd\u4f5c\u3067\u3042\u308b\u305f\u3081\u3002<\/li>\n<p><\/br><\/p>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\lambda f(x) dx = \\lambda \\int f(x) dx<\/span><\/span><\/br>\u3053\u3053\u3067 <span class=\"katex-eq\" data-katex-display=\"false\">\\lambda<\/span> \u306f\u4efb\u610f\u306e\u5b9f\u6570\u5b9a\u6570\u3067\u3059\u3002\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u8aac\u660e\u3055\u308c\u307e\u3059\uff1a<\/br>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} \\displaystyle \\int \\lambda \\dfrac{d\\phi(x)}{dx}dx &amp;=  \\displaystyle \\int \\dfrac{d}{dx}\\lambda \\phi(x) dx \\\\ \\\\\n\n&amp;= \\lambda \\phi(x) + C_1 \\\\ \\\\\n\n&amp;= \\lambda(\\phi(x) + C_2) \\\\ \\\\\n\n&amp;= \\lambda \\displaystyle  \\int \\frac{d\\phi(x)}{dx}dx \\end{array}<\/span>\n<p>\u305d\u3057\u3066\u3001<span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{d\\phi(x)}{dx}<\/span> \u3068\u7f6e\u304f\u3053\u3068\u3067<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\lambda f(x) dx = \\lambda \\int f(x)dx<\/span>\n<\/li>\n<p><\/br><\/p>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int f(x) + g(x) dx = \\int f(x) dx + \\int g(x) dx <\/span><\/span>\n<p>\u3053\u308c\u306f\u4e0a\u3068\u540c\u69d8\u306a\u65b9\u6cd5\u3067\u8a3c\u660e\u3067\u304d\u307e\u3059\u30022\u3064\u306e\u95a2\u6570 <span class=\"katex-eq\" data-katex-display=\"false\">\\phi(x)<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">\\psi(x)<\/span> \u3092\u8003\u3048\u3001\u305d\u308c\u305e\u308c\u6b21\u3092\u6e80\u305f\u3059\u3068\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{d\\phi(x)}{dx}<\/span> \u304a\u3088\u3073 <span class=\"katex-eq\" data-katex-display=\"false\">g(x) = \\dfrac{d\\psi(x)}{dx}<\/span>\n<p>\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n{} \\displaystyle \\int f(x) + g(x) dx\n\n&amp;= \\displaystyle \\int \\dfrac{d\\phi(x)}{dx} +  \\dfrac{d\\psi(x)}{dx} dx \\\\ \\\\\n\n&amp;= \\displaystyle \\int \\dfrac{d}{dx} (\\phi(x)  + \\psi(x)) dx \\\\ \\\\\n\n&amp;= \\phi(x) + \\psi(x) + C \\\\ \\\\\n\n&amp;= (\\phi(x) + C_1) + (\\psi(x) + C_2) \\\\ \\\\\n\n&amp;= \\displaystyle \\int \\dfrac{d\\phi(x)}{dx} dx + \\int \\dfrac{d\\psi(x)}{dx}dx \\\\ \\\\\n\n&amp;= \\displaystyle \\int f(x) dx + \\int g(x) dx\n\n\\end{array}<\/span>\n<\/li>\n<\/ol>\n<p><a name=\"3\"><\/a><\/p>\n<h2>\u57fa\u672c\u7684\u306a\u7a4d\u5206\u6280\u6cd5<\/h2>\n<p>\u57fa\u672c\u7684\u306a\u7a4d\u5206\u6280\u6cd5\u3092\u7528\u3044\u308b\u3053\u3068\u3067\u3001\u5c0e\u95a2\u6570\u306e\u7d50\u679c\u3092\u5229\u7528\u3057\u3066\u3044\u304f\u3064\u304b\u306e\u4e0d\u5b9a\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6280\u6cd5\u3092\u901a\u3058\u3066\u3001\u6b21\u306e\u3088\u3046\u306a\u7a4d\u5206\u306b\u6709\u7528\u306a\u7d50\u679c\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a<\/p>\n<h3>\u591a\u9805\u5f0f\u95a2\u6570\u306e\u7a4d\u5206<\/h3>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int 1 dx = x + C<\/span><\/span>\n<p dir=\"ltr\">\u306a\u305c\u306a\u3089 <span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} (x + C)= 1 <\/span> \u3060\u304b\u3089\u3067\u3059\u3002<\/p>\n<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int x^q dx = \\dfrac{x^{q+1}}{q+1}  + C,<\/span> \u305f\u3060\u3057 <span class=\"katex-eq\" data-katex-display=\"false\">q\\neq -1<\/span><\/span>\n<p>\u306a\u305c\u306a\u3089 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left(\\dfrac{x^{q+1}}{q+1}  + C\\right) = x^q<\/span><\/span> \u3060\u304b\u3089\u3067\u3059\u3002<\/p>\n<\/li>\n<\/ol>\n<p>\u3053\u308c\u3089\u306e\u7d50\u679c\u3068\u57fa\u672c\u7684\u6027\u8cea\u3092\u7d44\u307f\u5408\u308f\u305b\u308c\u3070\u3001\u4efb\u610f\u306e\u591a\u9805\u5f0f\u306e\u7a4d\u5206\u3092\u96e3\u306a\u304f\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<div style=\"background-color:#F3FFF3; padding:20px;\">\n<p><strong>\u4f8b\uff1a<\/strong><\/p>\n<ol>\n<li type=\"a\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\left( 3x+2 \\right) dx =  \\dfrac{3}{2}x^2 + 2x + C<\/span><\/span><\/li>\n<li type=\"a\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\left( 5x^2 + 2x + 3 \\right) dx= \\dfrac{5}{3}x^3 + x + 3x  + C<\/span><\/span><\/li>\n<li type=\"a\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\left( 4x^{12} - 7x^{-1\/3} + 1 \\right) dx  <\/span><\/span> <\/li>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} &amp;= \\dfrac{4}{13}x^{13} - \\dfrac{7}{2\/3}x^{2\/3} + x + C \\\\ \\\\\n\n&amp;= \\dfrac{4}{13}x^{13} - \\dfrac{21}{2}x^{2\/3} + x + C\n\n\\end{array}<\/span>\n<\/ol>\n<\/div>\n<h3>\u6307\u6570\u95a2\u6570\u3068\u5bfe\u6570\u95a2\u6570\u306e\u7a4d\u5206<\/h3>\n<p>\u6307\u6570\u95a2\u6570\u304a\u3088\u3073\u5bfe\u6570\u95a2\u6570\u306e\u5c0e\u95a2\u6570\u304b\u3089\u3001\u6b21\u306e\u57fa\u672c\u7684\u306a\u7a4d\u5206\u7d50\u679c\u304c\u5c0e\u304b\u308c\u307e\u3059\uff1a<\/p>\n<ol>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int e^{x}dx = e^{x} + C<\/span><\/span>\n<p>\u306a\u305c\u306a\u3089 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx}\\left(e^x + C\\right) = e^x<\/span><\/span> \u3060\u304b\u3089\u3067\u3059\u3002<\/p>\n<\/li>\n<li><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\dfrac{1}{x} dx = ln|x| + C<\/span><\/span>\n<p>\u306a\u305c\u306a\u3089 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx}\\left(ln|x| + C \\right) = \\dfrac{1}{|x|} sig(x) = \\dfrac{1}{x}<\/span><\/span> \u3060\u304b\u3089\u3067\u3059\u3002<\/p>\n<p>\u3053\u3053\u3067\u3001<span class=\"katex-eq\" data-katex-display=\"false\">sig(x)<\/span> \u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u7b26\u53f7\u95a2\u6570\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">sig(x) = \\left\\{\\begin{array}{} +1 &amp;,&amp;0\\lt x \\\\ -1 &amp;,&amp; x\\lt 0 \\end{array}\\right.<\/span>\n<\/li>\n<\/ol>\n<span class=\"katex-eq\" data-katex-display=\"false\">1\/x<\/span> \u306e\u7a4d\u5206\u7d50\u679c\u306b\u3088\u3063\u3066\u3001\u79c1\u305f\u3061\u306f\u3088\u308a\u5e83\u3044\u7bc4\u56f2\u306e\u95a2\u6570\u3092\u7a4d\u5206\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u3053\u308c\u306b\u3088\u308a\u591a\u9805\u5f0f\u306e\u6bd4\u3067\u69cb\u6210\u3055\u308c\u308b\u95a2\u6570\u306e\u7a4d\u5206\u304c\u53ef\u80fd\u306b\u306a\u308b\u304b\u3089\u3067\u3059\u3002<\/p>\n<div style=\"background-color:#F3FFF3; padding:20px;\">\n<p><strong>\u4f8b\uff1a<\/strong><\/p>\n<ol>\n<li type=\"a\"><\/br>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\displaystyle \\int \\dfrac{x^2 + 3x + 2}{5x^2}dx &amp;= \\displaystyle \\int \\dfrac{1}{5} + \\dfrac{3}{5}\\cdot \\dfrac{1}{x} + \\dfrac{2}{5}\\cdot\\dfrac{1}{x^2}dx \\\\ \\\\\n\n&amp;=\\dfrac{x}{5}+\\dfrac{3}{5}ln(x) - \\dfrac{2}{5}\\dfrac{1}{x} + C\n\n\\end{array}<\/span>\n<\/li>\n<p><\/br><\/p>\n<li type=\"a\"><\/br>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\displaystyle \\int \\dfrac{x^2 - 3 x + 2}{(x-2)^2}dx &amp;= \\displaystyle \\int \\dfrac{(x-2)^2 + (x-2)}{(x-2)^2} dx \\\\ \\\\\n\n&amp;= \\displaystyle \\int 1 + \\dfrac{1}{x-2} dx \\\\ \\\\\n\n&amp;= x + \\displaystyle \\int \\dfrac{1}{x-2}dx = x + ln|x-2| + C\n\n\\end{array}<\/span>\n<p>\u306a\u305c\u306a\u3089<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx}\\left( ln|x-2| + C\\right) = \\dfrac{1}{|x-2|}sig(x-2) = \\dfrac{1}{x-2}<\/span>\n<\/ol>\n<\/div>\n<h3>\u57fa\u672c\u7684\u306a\u53cc\u66f2\u7dda\u95a2\u6570\u306e\u7a4d\u5206<\/h3>\n<p>\u57fa\u672c\u7684\u306a\u53cc\u66f2\u7dda\u95a2\u6570\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} sinh(x) &amp;=&amp; \\dfrac{e^x - e^{-x}}{2} \\\\ \\\\\n\ncosh(x) &amp;=&amp; \\dfrac{e^x + e^{-x}}{2}\n\n\\end{array}<\/span>\n<p>\u6307\u6570\u95a2\u6570\u306e\u7a4d\u5206\u306e\u6271\u3044\u65b9\u3092\u3059\u3067\u306b\u5b66\u3093\u3060\u306e\u3067\u3001\u53cc\u66f2\u7dda\u6b63\u5f26\u95a2\u6570\u3068\u53cc\u66f2\u7dda\u4f59\u5f26\u95a2\u6570\u306e\u7a4d\u5206\u3082\u554f\u984c\u306a\u304f\u884c\u3048\u307e\u3059\u3002<\/p>\n<p>\u53cc\u66f2\u7dda\u6b63\u5f26\u95a2\u6570\u306e\u7a4d\u5206\u306f\u307b\u307c\u76f4\u63a5\u7684\u306b\u6c42\u3081\u3089\u308c\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rcl}\n\n{} \\displaystyle \\int sinh(x) dx\n\n&amp;=&amp; \\displaystyle \\int \\dfrac{e^x - e^{-x}}{2}dx \\\\ \\\\\n\n&amp;=&amp; \\dfrac{1}{2} \\left( \\displaystyle \\int e^x dx - \\int e^{-x}  dx \\right) \\\\ \\\\\n\n&amp;=&amp; \\dfrac{1}{2} \\left(e^x + e^{-x} \\right) + C = cosh(x) + C\n\n\\end{array}<\/span>\n<p>\u307e\u305f\u3001\u53cc\u66f2\u7dda\u4f59\u5f26\u95a2\u6570\u306e\u5834\u5408\u3082\u3001\u8a08\u7b97\u306f\u307b\u307c\u540c\u69d8\u3067\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} \\displaystyle \\int cosh(x) dx\n\n&amp;=&amp; \\displaystyle \\int \\dfrac{e^x + e^{-x}}{2}dx \\\\ \\\\\n\n&amp;=&amp; \\dfrac{1}{2} \\left( \\displaystyle \\int e^x dx + \\int e^{-x}  dx \\right) \\\\ \\\\\n\n&amp;=&amp; \\dfrac{1}{2} \\left(e^x - e^{-x} \\right) + C = sinh(x) + C\n\n\\end{array}<\/span>\n<p>\u3053\u308c\u3089\u306b\u52a0\u3048\u3066\u3001\u7a4d\u5206\u53ef\u80fd\u306a\u4ed6\u306e\u591a\u304f\u306e\u53cc\u66f2\u7dda\u95a2\u6570\u3082\u5b58\u5728\u3057\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} tanh(x) &amp;=&amp; \\dfrac{sinh(x)}{cosh(x)} \\\\\n\nsech(x) &amp;=&amp; \\dfrac{1}{cosh(x)} \\\\\n\n{}csch(x) &amp;=&amp; \\dfrac{1}{sinh(x)} \\\\\n\nctgh(x) &amp;=&amp; \\dfrac{1}{tanh(x)}\n\n\\end{array}<\/span>\n<p>\u305f\u3060\u3057\u3001\u3053\u308c\u3089\u306e\u7a4d\u5206\u306b\u306f\u4ed6\u306e\u6280\u6cd5\u304c\u5fc5\u8981\u3067\u3042\u308a\u3001\u305d\u308c\u306b\u3064\u3044\u3066\u306f\u4eca\u5f8c\u306e\u8b1b\u7fa9\u3067\u5b66\u3093\u3067\u3044\u304d\u307e\u3059\u3002<\/p>\n<h3>\u57fa\u672c\u7684\u306a\u4e09\u89d2\u95a2\u6570\u306e\u7a4d\u5206<\/h3>\n<p>\u57fa\u672c\u7684\u306a\u4e09\u89d2\u95a2\u6570\u306f <span class=\"katex-eq\" data-katex-display=\"false\">sin(x)<\/span> \u3068 <span class=\"katex-eq\" data-katex-display=\"false\">cos(x)<\/span> \u3067\u3059\u3002\u305d\u308c\u3089\u306e\u7a4d\u5206\u306f\u3001\u5c0e\u95a2\u6570\u306b\u95a2\u3059\u308b\u65e2\u77e5\u306e\u7d50\u679c\u304b\u3089\u307b\u307c\u76f4\u63a5\u7684\u306b\u6c42\u3081\u3089\u308c\u307e\u3059\u3002<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{} \\displaystyle \\int sin(x) dx = -cos(x) + C \\\\ \\\\\n\n{} \\displaystyle \\int cos(x) dx = sen(x) + C\n\n\\end{array}<\/span>\n<p>\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u78ba\u8a8d\u3067\u304d\u307e\u3059\uff1a<\/p>\n<p style=\"text-align:center;\" dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\n\n{}  \\dfrac{d}{dx}\\left( sin(x) + C \\right) &amp;=&amp; cos(x) \\\\ \\\\\n\n{}  \\dfrac{d}{dx}\\left( cos(x) + C \\right) &amp;=&amp; -sin(x) \\\\ \\\\\n\n\\end{array}<\/span>\n<h2>\u7d50\u8ad6<\/h2>\n<p>\u3053\u306e\u8b1b\u7fa9\u3067\u306f\u3001\u4e0d\u5b9a\u7a4d\u5206\u306b\u3064\u3044\u3066\u3001\u7406\u8ad6\u7684\u306a\u57fa\u790e\u304b\u3089\u6700\u3082\u57fa\u672c\u7684\u306a\u5b9f\u7528\u7684\u5fdc\u7528\u306b\u81f3\u308b\u307e\u3067\u3092\u6982\u89b3\u3057\u307e\u3057\u305f\u3002\u4e0d\u5b9a\u7a4d\u5206\u3092\u5c0e\u95a2\u6570\u306e\u9006\u64cd\u4f5c\u3068\u3057\u3066\u7406\u89e3\u3057\u3001\u305d\u306e\u57fa\u672c\u7684\u6027\u8cea\u3092\u7279\u5b9a\u3057\u3001\u591a\u9805\u5f0f\u95a2\u6570\u3001\u6307\u6570\u95a2\u6570\u3001\u5bfe\u6570\u95a2\u6570\u3001\u53cc\u66f2\u7dda\u95a2\u6570\u3001\u4e09\u89d2\u95a2\u6570\u306e\u7c21\u5358\u306a\u7a4d\u5206\u306b\u76f4\u63a5\u9069\u7528\u3059\u308b\u6280\u6cd5\u3092\u5b66\u3073\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u77e5\u8b58\u306f\u3001\u5c06\u6765\u7684\u306b\u3088\u308a\u8907\u96d1\u306a\u7a4d\u5206\u554f\u984c\u306b\u53d6\u308a\u7d44\u3080\u305f\u3081\u306e\u672c\u8cea\u7684\u306a\u57fa\u76e4\u3092\u63d0\u4f9b\u3057\u3001\u7269\u7406\u5b66\u3001\u5de5\u5b66\u3001\u305d\u306e\u4ed6\u306e\u79d1\u5b66\u306b\u304a\u3051\u308b\u5fdc\u7528\u306e\u305f\u3081\u306b\u3082\u4e0d\u53ef\u6b20\u306a\u3082\u306e\u3068\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u57fa\u790e\u3092\u3082\u3068\u306b\u3001\u4eca\u5f8c\u306e\u8b1b\u7fa9\u3067\u306f\u3055\u3089\u306b\u9ad8\u5ea6\u306a\u6280\u6cd5\u3092\u5c0e\u5165\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e0d\u5b9a\u7a4d\u5206\u3068\u57fa\u672c\u7684\u306a\u7a4d\u5206\u6280\u6cd5 \u3053\u306e\u8b1b\u7fa9\u3067\u306f\u3001\u6700\u3082\u57fa\u672c\u7684\u306a\u4e0d\u5b9a\u7a4d\u5206\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306e\u57fa\u672c\u7684\u306a\u6280\u6cd5\u3001\u304a\u3088\u3073\u7a4d\u5206\u6f14\u7b97\u5b50\u306e\u6027\u8cea\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u306f\u3001\u591a\u9805\u5f0f\u3001\u6307\u6570\u95a2\u6570\u3001\u53cc\u66f2\u7dda\u95a2\u6570\u3001\u4e09\u89d2\u95a2\u6570\u306e\u57fa\u672c\u7684\u306a\u7a4d\u5206\u304c\u542b\u307e\u308c\u307e\u3059\u3002 \u5b66\u7fd2\u76ee\u6a19:\u3053\u306e\u8b1b\u7fa9\u306e\u7d42\u4e86\u6642\u306b\u306f\u3001\u5b66\u751f\u306f\u4ee5\u4e0b\u306e\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 \u7406\u89e3\u3059\u308b\uff1a\u4e0d\u5b9a\u7a4d\u5206\u306e\u30d7\u30ed\u30bb\u30b9\u3092\u5fae\u5206\u306e\u9006\u904e\u7a0b\u3068\u3057\u3066\u7406\u89e3\u3059\u308b\u3002 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