{"id":32665,"date":"2023-04-04T13:00:49","date_gmt":"2023-04-04T13:00:49","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=32665"},"modified":"2025-03-27T12:25:09","modified_gmt":"2025-03-27T12:25:09","slug":"%d0%bd%d0%b5%d0%be%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%91%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b8%d0%bd%d1%82%d0%b5%d0%b3%d1%80%d0%b0%d0%bb%d1%8b-%d0%b8-%d0%b1%d0%b0%d0%b7%d0%be%d0%b2%d1%8b%d0%b5-%d0%bc","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/ru\/%d0%bd%d0%b5%d0%be%d0%bf%d1%80%d0%b5%d0%b4%d0%b5%d0%bb%d1%91%d0%bd%d0%bd%d1%8b%d0%b5-%d0%b8%d0%bd%d1%82%d0%b5%d0%b3%d1%80%d0%b0%d0%bb%d1%8b-%d0%b8-%d0%b1%d0%b0%d0%b7%d0%be%d0%b2%d1%8b%d0%b5-%d0%bc\/","title":{"rendered":"\u041d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u0438 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f"},"content":{"rendered":"<style>\n    p, ul, ol {\n        text-align: justify;\n    }\n    h1, h2, h3 {\n    text-align:center;\n    }\n<\/style>\n<p><center><\/p>\n<h1>\u041d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u0438 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f<\/h1>\n<p><\/center><\/p>\n<p style=\"text-align:center;\">\u0412 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u0432\u0432\u043e\u0434\u044f\u0442\u0441\u044f \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0441\u0430\u043c\u044b\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u044b\u0445 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0445 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u043e\u0432, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f. \u042d\u0442\u043e \u043e\u0445\u0432\u0430\u0442\u044b\u0432\u0430\u0435\u0442 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0435, \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435, \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b.<\/p>\n<p style=\"text-align:center;\"><strong><u>\u0426\u0435\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f<\/u>:<\/strong><br \/>\u041f\u043e \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u0437\u0430\u043d\u044f\u0442\u0438\u044f \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0431\u0443\u0434\u0435\u0442 \u0441\u043f\u043e\u0441\u043e\u0431\u0435\u043d<\/p>\n<ol>\n<li><strong>\u041f\u043e\u043d\u044f\u0442\u044c<\/strong> \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u043e\u0433\u043e \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043a\u0430\u043a \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u043f\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u043a \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044e.<\/li>\n<li><strong>\u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c<\/strong> \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u043e\u0432 \u0438 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0439, \u0441\u043e\u0434\u0435\u0440\u0436\u0430\u0449\u0438\u0445 \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435, \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/li>\n<li><strong>\u0418\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u0442\u044c<\/strong> \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u043e\u0432 \u0434\u043b\u044f \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u0438\u044f \u0430\u043b\u0433\u0435\u0431\u0440\u0430\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u0440\u0435\u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0439, \u043e\u0431\u043b\u0435\u0433\u0447\u0430\u044e\u0449\u0438\u0445 \u0438\u0445 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u0421\u041e\u0414\u0415\u0420\u0416\u0410\u041d\u0418\u0415<\/strong><br \/>\n<a href=\"#1\">\u0417\u041d\u0410\u0427\u0415\u041d\u0418\u0415 \u041d\u0415\u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0401\u041d\u041d\u042b\u0425 \u0418\u041d\u0422\u0415\u0413\u0420\u0410\u041b\u041e\u0412<\/a><br \/>\n<a href=\"#2\">\u0410\u041d\u0422\u0418\u041f\u0420\u041e\u0418\u0417\u0412\u041e\u0414\u041d\u042b\u0415, \u041d\u0415\u041e\u041f\u0420\u0415\u0414\u0415\u041b\u0401\u041d\u041d\u042b\u0415 \u0418\u041d\u0422\u0415\u0413\u0420\u0410\u041b\u042b \u0418 \u041f\u0415\u0420\u0412\u041e\u041e\u0411\u0420\u0410\u0417\u041d\u042b\u0415 \u0424\u0423\u041d\u041a\u0426\u0418\u0419<\/a><br \/>\n<a href=\"#3\">\u0411\u0410\u0417\u041e\u0412\u042b\u0415 \u041c\u0415\u0422\u041e\u0414\u042b \u0418\u041d\u0422\u0415\u0413\u0420\u0418\u0420\u041e\u0412\u0410\u041d\u0418\u042f<\/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>\u0417\u043d\u0430\u0447\u0435\u043d\u0438\u0435 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0445 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u043e\u0432<\/h2>\n<p>\u041d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u0430\u043b\u044c\u043d\u044b\u043c \u0438\u043d\u0441\u0442\u0440\u0443\u043c\u0435\u043d\u0442\u043e\u043c \u0432 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u043e\u043c \u0430\u043d\u0430\u043b\u0438\u0437\u0435 \u0438 \u0438\u043c\u0435\u044e\u0442 \u0448\u0438\u0440\u043e\u043a\u0438\u0439 \u0441\u043f\u0435\u043a\u0442\u0440 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0439 \u0432 \u0444\u0438\u0437\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0438 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043d\u0430\u0443\u043a\u0430\u0445. \u041e\u043d\u0438 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0442 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u0443\u044e \u0434\u0430\u043d\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0447\u0442\u043e, \u0432 \u0441\u0432\u043e\u044e \u043e\u0447\u0435\u0440\u0435\u0434\u044c, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043f\u043b\u043e\u0449\u0430\u0434\u0435\u0439 \u043f\u043e\u0434 \u043a\u0440\u0438\u0432\u044b\u043c\u0438, \u043e\u0431\u044a\u0451\u043c\u043e\u0432 \u0442\u0435\u043b, \u0440\u0430\u0441\u0447\u0451\u0442\u0430 \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e\u0441\u0442\u0435\u0439 \u0438 \u043c\u043d\u043e\u0433\u0438\u0445 \u0434\u0440\u0443\u0433\u0438\u0445 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0439 \u0432 \u0444\u0438\u0437\u0438\u043a\u0435, \u0438\u043d\u0436\u0435\u043d\u0435\u0440\u0438\u0438, \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0435 \u0438 \u044d\u043a\u043e\u043d\u043e\u043c\u0438\u043a\u0435. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u0438\u0433\u0440\u0430\u044e\u0442 \u043a\u043b\u044e\u0447\u0435\u0432\u0443\u044e \u0440\u043e\u043b\u044c \u0432 \u0440\u0435\u0448\u0435\u043d\u0438\u0438 \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0439, \u0447\u0442\u043e \u0434\u0435\u043b\u0430\u0435\u0442 \u0438\u0445 \u043d\u0435\u0437\u0430\u043c\u0435\u043d\u0438\u043c\u044b\u043c\u0438 \u0432\u043e \u043c\u043d\u043e\u0433\u0438\u0445 \u043e\u0431\u043b\u0430\u0441\u0442\u044f\u0445 \u043d\u0430\u0443\u043a\u0438 \u0438 \u0442\u0435\u0445\u043d\u0438\u043a\u0438.<\/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>\u0410\u043d\u0442\u0438\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435, \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u0438 \u043f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/h2>\n<p>\u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f <span class=\"katex-eq\" data-katex-display=\"false\">F(x)<\/span> \u0438\u043c\u0435\u0435\u0442 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0443\u044e <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u043d\u0430 \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span>, \u0442\u043e \u0433\u043e\u0432\u043e\u0440\u044f\u0442, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">F(x)<\/span> \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u043d\u0430 \u044d\u0442\u043e\u043c \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435.<\/p>\n<p>\u0412\u0430\u0436\u043d\u043e \u043f\u043e\u043c\u043d\u0438\u0442\u044c, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">F(x)<\/span> \u2014 \u043f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">f(x),<\/span> \u0442\u043e \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">F(x) + C,<\/span> \u0433\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u2014 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u0430\u044f \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0430, \u0442\u0430\u043a\u0436\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u043e\u0439. \u042d\u0442\u043e \u0437\u0430\u043f\u0438\u0441\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int f(x) dx = F(x) + C<\/span>\n<p>\u041a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">C<\/span> \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f <strong>\u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u043e\u0439 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f<\/strong>, \u0438 \u0435\u0451 \u043d\u0430\u043b\u0438\u0447\u0438\u0435 \u0443\u043a\u0430\u0437\u044b\u0432\u0430\u0435\u0442 \u043d\u0430 \u0442\u043e, \u0447\u0442\u043e \u043f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u043d\u0435 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0430 \u0446\u0435\u043b\u043e\u0435 \u0441\u0435\u043c\u0435\u0439\u0441\u0442\u0432\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u0439: \u043c\u043d\u043e\u0436\u0435\u0441\u0442\u0432\u043e \u0432\u0441\u0435\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f \u043a\u043e\u0442\u043e\u0440\u044b\u0445 \u0440\u0430\u0432\u043d\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u043d\u0430 \u0438\u043d\u0442\u0435\u0440\u0432\u0430\u043b\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span>.<\/p>\n<p>\u0421\u043b\u043e\u0432\u0430 \u0430\u043d\u0442\u0438\u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u0430\u044f, \u043f\u0435\u0440\u0432\u043e\u043e\u0431\u0440\u0430\u0437\u043d\u0430\u044f \u0438 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0439 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u0440\u0430\u0437\u043d\u044b\u043c\u0438 \u0441\u043f\u043e\u0441\u043e\u0431\u0430\u043c\u0438 \u0432\u044b\u0440\u0430\u0437\u0438\u0442\u044c \u043e\u0434\u043d\u0443 \u0438 \u0442\u0443 \u0436\u0435 \u0438\u0434\u0435\u044e, \u0438 \u043c\u044b \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u043c \u0438\u0445 \u043a\u0430\u043a \u0441\u0438\u043d\u043e\u043d\u0438\u043c\u044b. \u0412 \u0441\u0443\u0449\u043d\u043e\u0441\u0442\u0438, \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0439 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b \u2014 \u044d\u0442\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u043f\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u043a \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044e \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u043e\u0439, \u0438 \u0438\u043c\u0435\u043d\u043d\u043e \u0438\u0437 \u044d\u0442\u043e\u0439 \u0438\u0434\u0435\u0438 \u0441\u043b\u0435\u0434\u0443\u044e\u0442 \u0435\u0433\u043e \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430.<\/p>\n<h3>\u0411\u0430\u0437\u043e\u0432\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0445 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u043e\u0432<\/h3>\n<p>\u0427\u0442\u043e\u0431\u044b \u0443\u043c\u0435\u0442\u044c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0441\u043d\u0430\u0447\u0430\u043b\u0430 \u0437\u043d\u0430\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0435\u043f\u043e\u0441\u0440\u0435\u0434\u0441\u0442\u0432\u0435\u043d\u043d\u043e \u043d\u0430\u0441\u043b\u0435\u0434\u0443\u044e\u0442\u0441\u044f \u043e\u0442 \u0441\u0432\u043e\u0439\u0441\u0442\u0432 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445.<\/p>\n<ol>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int  \\dfrac{df(x)}{dx} dx = f(x) + C<\/span><\/br>\u041f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0439 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b \u2014 \u044d\u0442\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u043a \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044e.<\/li>\n<p><\/br><\/p>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\lambda f(x) dx = \\lambda \\int f(x) dx<\/span><\/br>\u0413\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">\\lambda<\/span> \u2014 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u043b\u044c\u043d\u0430\u044f \u0432\u0435\u0449\u0435\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f \u043a\u043e\u043d\u0441\u0442\u0430\u043d\u0442\u0430. \u042d\u0442\u043e \u043f\u0440\u043e\u0438\u0441\u0445\u043e\u0434\u0438\u0442 \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e<\/br><br \/>\n<center><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\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><\/center><br \/>\n<\/br><br \/>\n\u0410 \u0437\u0430\u0442\u0435\u043c, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f <span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{d\\phi(x)}{dx}<\/span>, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c<\/br><br \/>\n<center><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\lambda f(x) dx = \\lambda \\int f(x)dx<\/span><\/center><\/li>\n<p><\/br><\/p>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int f(x) + g(x) dx = \\int f(x) dx + \\int g(x) dx <\/span>\n<\/br><br \/>\n\u042d\u0442\u043e \u043c\u043e\u0436\u043d\u043e \u0434\u043e\u043a\u0430\u0437\u0430\u0442\u044c \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u043e \u043f\u0440\u0435\u0434\u044b\u0434\u0443\u0449\u0435\u043c\u0443. \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u0434\u0432\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\phi(x)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">\\psi(x)<\/span>, \u0442\u0430\u043a\u0438\u0435 \u0447\u0442\u043e<br \/>\n<\/br><br \/>\n<center><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = \\dfrac{d\\phi(x)}{dx}<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">g(x) = \\dfrac{d\\psi(x)}{dx}<\/span><\/center><br \/>\n<\/br><br \/>\n\u0422\u043e\u0433\u0434\u0430 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c<br \/>\n<\/br><br \/>\n<center><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\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><\/center>\n<\/li>\n<\/ol>\n<p><a name=\"3\"><\/a><br \/>\n<\/br><\/br><\/p>\n<h2>\u0411\u0430\u0437\u043e\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f<\/h2>\n<p>\u0421\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043f\u043e\u0437\u0432\u043e\u043b\u044f\u044e\u0442 \u043d\u0430\u043c \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u043d\u0435\u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f. \u0421 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u044d\u0442\u0438\u0445 \u043c\u0435\u0442\u043e\u0434\u043e\u0432 \u043c\u043e\u0436\u043d\u043e \u043f\u043e\u043b\u0443\u0447\u0438\u0442\u044c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043f\u043e\u043b\u0435\u0437\u043d\u044b\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b \u0434\u043b\u044f \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f:<\/p>\n<h3>\u0418\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/h3>\n<ol>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int 1 dx = x + C<\/span>\n<\/br><br \/>\n\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} (x + C)= 1 <\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int x^q dx = \\dfrac{x^{q+1}}{q+1}  + C,<\/span> \u043f\u0440\u0438 \u0443\u0441\u043b\u043e\u0432\u0438\u0438, \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">q\\neq -1<\/span>\n<\/br><br \/>\n\u041f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left(\\dfrac{x^{q+1}}{q+1}  + C\\right) = x^q.<\/span>\n<\/li>\n<\/ol>\n<p>\u0421 \u044d\u0442\u0438\u043c\u0438 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0430\u043c\u0438 \u0438 \u0431\u0430\u0437\u043e\u0432\u044b\u043c\u0438 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430\u043c\u0438 \u043c\u043e\u0436\u043d\u043e \u0431\u0435\u0437 \u0442\u0440\u0443\u0434\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u043b\u044e\u0431\u044b\u0445 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u043e\u0432.<\/p>\n<div style=\"background-color:#F3FFF3; padding:20px;\">\n<p><strong>\u041f\u0440\u0438\u043c\u0435\u0440:<\/strong><\/p>\n<ol>\n<li type=\"a\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\left( 3x+2 \\right) dx =  \\dfrac{3}{2}x^2 + 2x + C<\/span><\/li>\n<li type=\"a\"><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><\/li>\n<li type=\"a\"> <span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\left( 4x^{12} - 7x^{-1\/3} + 1 \\right) dx  <\/span> <\/li>\n<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>\u0418\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u043e\u0439 \u0438 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0447\u0435\u0441\u043a\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/h3>\n<p>\u0418\u0441\u0445\u043e\u0434\u044f \u0438\u0437 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0445 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u043e\u0432 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0445 \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0445 \u0438 \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439, \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0435 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u044b:<\/p>\n<ol>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int e^{x}dx = e^{x} + C<\/span>\n<br \/>\n\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx}\\left(e^x + C\\right) = e^x<\/span>\n<\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\dfrac{1}{x} dx = ln|x| + C<\/span>\n<\/br><br \/>\n\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 <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>\n<\/br><br \/>\n\u0413\u0434\u0435 <span class=\"katex-eq\" data-katex-display=\"false\">sig(x)<\/span> \u2014 \u044d\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0437\u043d\u0430\u043a\u0430, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u0430\u044f \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c:<br \/>\n<\/br><br \/>\n<center><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><\/center>\n<\/li>\n<\/ol>\n<p>\u0420\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u0430 <span class=\"katex-eq\" data-katex-display=\"false\">1\/x<\/span> \u0440\u0430\u0441\u0448\u0438\u0440\u044f\u0435\u0442 \u043d\u0430\u0448\u0438 \u0432\u043e\u0437\u043c\u043e\u0436\u043d\u043e\u0441\u0442\u0438 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0442\u0435\u043f\u0435\u0440\u044c \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u043d\u0430\u0447\u0438\u043d\u0430\u0442\u044c \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c \u0434\u0440\u043e\u0431\u043d\u044b\u0435 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u044f \u0441 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0430\u043c\u0438.<\/p>\n<div style=\"background-color:#F3FFF3; padding:20px;\">\n<p><strong>\u041f\u0440\u0438\u043c\u0435\u0440:<\/strong><\/p>\n<ol>\n<li type=\"a\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\dfrac{x^2 + 3x + 2}{5x^2}dx = \\int \\dfrac{1}{5} + \\dfrac{3}{5}\\dfrac{1}{x} + \\dfrac{2}{5}\\dfrac{1}{x^2}dx<\/span>\n<\/br><br \/>\n<span class=\"katex-eq\" data-katex-display=\"false\">=\\dfrac{x}{5}+\\dfrac{3}{5}ln(x) - \\dfrac{2}{5}\\dfrac{1}{x} + C <\/span><\/li>\n<p><\/br><\/p>\n<li type=\"a\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\int \\dfrac{x^2 - 3 x + 2}{(x-2)^2}dx = \\int \\dfrac{(x-2)^2 + (x-2)}{(x-2)^2} dx<\/span><\/li>\n<p><\/br><br \/>\n<span class=\"katex-eq\" data-katex-display=\"false\">= \\displaystyle \\int 1 + \\dfrac{1}{x-2} dx\\\\ \\\\\n\n= x + \\displaystyle \\int \\dfrac{1}{x-2}dx = x + ln|x-2| + C<\/span>\n<\/br><br \/>\n\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443<br \/>\n<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>\u0418\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u0431\u0430\u0437\u043e\u0432\u044b\u0445 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/h3>\n<p>\u0411\u0430\u0437\u043e\u0432\u044b\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u044d\u0442\u043e<\/p>\n<p style=\"text-align:center;\"><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>\u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043c\u044b \u0443\u0436\u0435 \u0437\u043d\u0430\u0435\u043c, \u043a\u0430\u043a \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u043d\u0435 \u0431\u0443\u0434\u0435\u0442 \u043d\u0438\u043a\u0430\u043a\u0438\u0445 \u0442\u0440\u0443\u0434\u043d\u043e\u0441\u0442\u0435\u0439 \u0441 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u0430\u043c\u0438 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 \u0438 \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430.<\/p>\n<p>\u0414\u043b\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0438\u043d\u0443\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u0435 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438 \u043f\u0440\u044f\u043c\u043e\u0435:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}\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>\u0410 \u0434\u043b\u044f \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u043a\u043e\u0441\u0438\u043d\u0443\u0441\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0430\u043d\u0430\u043b\u043e\u0433\u0438\u0447\u043d\u044b:<\/p>\n<p style=\"text-align:center;\"><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>\u041a\u0440\u043e\u043c\u0435 \u044d\u0442\u0438\u0445, \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u044e\u0442 \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u043e\u0436\u043d\u043e \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u0442\u044c:<\/p>\n<p style=\"text-align:center;\"><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>\u041e\u0434\u043d\u0430\u043a\u043e \u0434\u043b\u044f \u0438\u0445 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043d\u0443\u0436\u043d\u044b \u0434\u0440\u0443\u0433\u0438\u0435 \u043c\u0435\u0442\u043e\u0434\u044b, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043c\u044b \u0440\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0437\u0430\u043d\u044f\u0442\u0438\u044f\u0445.<\/p>\n<h3>\u0418\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u0431\u0430\u0437\u043e\u0432\u044b\u0445 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0444\u0443\u043d\u043a\u0446\u0438\u0439<\/h3>\n<p>\u0411\u0430\u0437\u043e\u0432\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u2014 \u044d\u0442\u043e <span class=\"katex-eq\" data-katex-display=\"false\">sin(x)<\/span> \u0438 <span class=\"katex-eq\" data-katex-display=\"false\">cos(x)<\/span>. \u0418\u0445 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043d\u0430\u043f\u0440\u044f\u043c\u0443\u044e, \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435:<\/p>\n<p style=\"text-align:center;\"><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>\u042d\u0442\u043e \u043f\u043e\u0442\u043e\u043c\u0443 \u0447\u0442\u043e<\/p>\n<p style=\"text-align:center;\"><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>\u0417\u0430\u043a\u043b\u044e\u0447\u0435\u043d\u0438\u0435<\/h2>\n<p>\u041d\u0430 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u043c\u044b \u0438\u0437\u0443\u0447\u0438\u043b\u0438 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u2014 \u043e\u0442 \u0438\u0445 \u0442\u0435\u043e\u0440\u0435\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043e\u0441\u043d\u043e\u0432 \u0434\u043e \u043f\u0440\u043e\u0441\u0442\u0435\u0439\u0448\u0438\u0445 \u043f\u0440\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0439. \u041c\u044b \u0443\u0437\u043d\u0430\u043b\u0438, \u0447\u0442\u043e \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0435 \u2014 \u044d\u0442\u043e \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u043f\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u043a \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044e, \u0438\u0437\u0443\u0447\u0438\u043b\u0438 \u0438\u0445 \u043e\u0441\u043d\u043e\u0432\u043d\u044b\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u0438 \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043b\u0438 \u043f\u0440\u044f\u043c\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043a \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u043c, \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u043c, \u043b\u043e\u0433\u0430\u0440\u0438\u0444\u043c\u0438\u0447\u0435\u0441\u043a\u0438\u043c, \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0438 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u043c \u0444\u0443\u043d\u043a\u0446\u0438\u044f\u043c. \u042d\u0442\u0438 \u0437\u043d\u0430\u043d\u0438\u044f \u044f\u0432\u043b\u044f\u044e\u0442\u0441\u044f \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u043c \u0444\u0443\u043d\u0434\u0430\u043c\u0435\u043d\u0442\u043e\u043c \u0434\u043b\u044f \u0440\u0435\u0448\u0435\u043d\u0438\u044f \u0431\u043e\u043b\u0435\u0435 \u0441\u043b\u043e\u0436\u043d\u044b\u0445 \u0437\u0430\u0434\u0430\u0447 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u0432 \u0431\u0443\u0434\u0443\u0449\u0435\u043c \u0438 \u0431\u0443\u0434\u0443\u0442 \u043a\u0440\u0430\u0439\u043d\u0435 \u0432\u0430\u0436\u043d\u044b \u0434\u043b\u044f \u0438\u0437\u0443\u0447\u0435\u043d\u0438\u044f \u043f\u0440\u043e\u0434\u0432\u0438\u043d\u0443\u0442\u044b\u0445 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u0439 \u0432 \u0444\u0438\u0437\u0438\u043a\u0435, \u0438\u043d\u0436\u0435\u043d\u0435\u0440\u0438\u0438 \u0438 \u0434\u0440\u0443\u0433\u0438\u0445 \u043d\u0430\u0443\u043a\u0430\u0445. \u0411\u043b\u0430\u0433\u043e\u0434\u0430\u0440\u044f \u044d\u0442\u043e\u043c\u0443 \u0431\u0430\u0437\u043e\u0432\u043e\u043c\u0443 \u043f\u043e\u043d\u0438\u043c\u0430\u043d\u0438\u044e \u043c\u044b \u0441\u043c\u043e\u0436\u0435\u043c \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043a \u0431\u043e\u043b\u0435\u0435 \u043f\u0440\u043e\u0434\u0432\u0438\u043d\u0443\u0442\u044b\u043c \u043c\u0435\u0442\u043e\u0434\u0430\u043c \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u0445 \u0437\u0430\u043d\u044f\u0442\u0438\u044f\u0445.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u041d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u0438 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u0412 \u044d\u0442\u043e\u043c \u0437\u0430\u043d\u044f\u0442\u0438\u0438 \u0432\u0432\u043e\u0434\u044f\u0442\u0441\u044f \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u0441\u0430\u043c\u044b\u0445 \u044d\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u0440\u043d\u044b\u0445 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0445 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u043e\u0432, \u0430 \u0442\u0430\u043a\u0436\u0435 \u0441\u0432\u043e\u0439\u0441\u0442\u0432\u0430 \u043e\u043f\u0435\u0440\u0430\u0442\u043e\u0440\u0430 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f. \u042d\u0442\u043e \u043e\u0445\u0432\u0430\u0442\u044b\u0432\u0430\u0435\u0442 \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u0438\u0430\u043b\u044c\u043d\u044b\u0435, \u044d\u043a\u0441\u043f\u043e\u043d\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u044b\u0435, \u0433\u0438\u043f\u0435\u0440\u0431\u043e\u043b\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u0442\u0440\u0438\u0433\u043e\u043d\u043e\u043c\u0435\u0442\u0440\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b. \u0426\u0435\u043b\u0438 \u043e\u0431\u0443\u0447\u0435\u043d\u0438\u044f:\u041f\u043e \u0437\u0430\u0432\u0435\u0440\u0448\u0435\u043d\u0438\u0438 \u044d\u0442\u043e\u0433\u043e \u0437\u0430\u043d\u044f\u0442\u0438\u044f \u0441\u0442\u0443\u0434\u0435\u043d\u0442 \u0431\u0443\u0434\u0435\u0442 \u0441\u043f\u043e\u0441\u043e\u0431\u0435\u043d \u041f\u043e\u043d\u044f\u0442\u044c \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u043d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u043e\u0433\u043e \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f \u043a\u0430\u043a \u043e\u0431\u0440\u0430\u0442\u043d\u044b\u0439 \u043f\u0440\u043e\u0446\u0435\u0441\u0441 \u043f\u043e \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044e \u043a \u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044e. \u0412\u044b\u0447\u0438\u0441\u043b\u044f\u0442\u044c \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u043f\u043e\u043b\u0438\u043d\u043e\u043c\u043e\u0432 \u0438 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0439, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":32629,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":11,"footnotes":""},"categories":[1143,573],"tags":[],"class_list":["post-32665","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-1143","category-573"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>\u041d\u0435\u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0451\u043d\u043d\u044b\u0435 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u044b \u0438 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 \u043c\u0435\u0442\u043e\u0434\u044b \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u044f - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u041e\u0441\u0432\u043e\u0439 \u0431\u0430\u0437\u043e\u0432\u044b\u0435 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