{"id":11574,"date":"2021-02-23T12:32:28","date_gmt":"2021-02-23T07:02:28","guid":{"rendered":"https:\/\/learnsteer.sasnaka.org\/science\/?p=11574"},"modified":"2021-10-12T23:19:57","modified_gmt":"2021-10-12T17:49:57","slug":"04-05-01-2","status":"publish","type":"post","link":"https:\/\/learnsteer.sasnaka.org\/science\/advanced-level-science\/combined-mathematics\/04-05-01-2\/","title":{"rendered":"04.05.01 &#8211; \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba\u0dda \u0dc4\u0dd0\u0db3\u0dd2\u0db1\u0dca\u0dc0\u0dd3\u0db8 \u0dc4\u0dcf \u0db8\u0dd6\u0dbd\u0dd2\u0d9a \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba\u0db1\u0dca"},"content":{"rendered":"\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?id=1zaYSXmmKtEI7L634oT3ufxFF4YbXDqbX&amp;export=download\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li><strong><span class=\"has-inline-color has-vivid-red-color\">\u0dc3\u0d82\u0dba\u0dd4\u0d9a\u0dca\u0dad \u0d9c\u0dab\u0dd2\u0dad\u0dba I \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dad\u0dca\u200d\u0dbb\u0dba\u0dda A \u0d9a\u0ddc\u0da7\u0dc3\u0dda \u0dbd\u0d9a\u0dd4\u0dab\u0dd4 25 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0d9a\u0dca \u0dc3\u0dc4 B \u0d9a\u0ddc\u0da7\u0dc3\u0dda (\u0dbb\u0da0\u0db1\u0dcf \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1) \u0d9c\u0dd0\u0da7\u0dc5\u0dd4\u0dc0\u0d9a \u0db8\u0dd9\u0db8 \u0db4\u0dcf\u0da9\u0db8\u0dd9\u0dc4\u0dd2 \u0dc3\u0dd2\u0daf\u0dca\u0db0\u0dcf\u0db1\u0dca\u0dad \u0d87\u0dad\u0dd4\u0dbd\u0dad\u0dca \u0dc0\u0dda.<\/span><\/strong><\/li>\r\n<li><strong><span class=\"has-inline-color has-vivid-red-color\">\u0db8\u0dd9\u0db8 \u0db4\u0dcf\u0da9\u0db8 \u0dc3\u0db3\u0dc4\u0dcf \u0d85\u0dc0\u0d9a\u0dbd\u0db1\u0dba \u0dc4\u0dcf \u0dad\u0dca\u200d\u0dbb\u0dd2\u0d9a\u0ddd\u0dab\u0db8\u0dd2\u0dad\u0dd2\u0dba \u0daf\u0dd0\u0db1\u0dd4\u0db8 \u0d85\u0dc0\u0dc1\u0dca\u200d\u0dba\u0dc0\u0dda.<\/span><\/strong><\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\"><strong>\u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba\u0dda \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd3\u0db8<\/strong><\/h3>\r\n\r\n\r\n\r\n<p>g(x) \u0dba\u0db1\u0dd4 X \u0dc4\u0dd2 \u0d85\u0dc0\u0d9a\u0dbd\u0dca\u200d\u0dba \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad\u0dba\u0d9a\u0dca\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\frac d{dx}<\/span>\u00a0g(x)= f(x)\u00a0 \u0daf \u0db1\u0db8\u0dca, x \u0dc0\u0dd2\u0dc2\u0dba\u0dd9\u0db1\u0dca f(x)\u00a0 \u0dc4\u0dd2 \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba g(x) \u0dc0\u0dda. \u00a0\u0db8\u0dd9\u0dba \u00a0\u222bf(x)dx= g(x) \u200c \u0dbd\u0dd9\u0dc3 \u0dbd\u0dd2\u0dba\u0db1\u0dd4 \u0dbd\u0db6\u0db1 \u0d85\u0dad\u0dbb\u00a0 f(x)\u00a0 \u0daf\u0dd3 \u0d87\u0dad\u0dd2 \u0dc0\u0dd2\u0da7 g(x) \u0dc3\u0dd9\u0dc0\u0dd3\u0db8\u0dda \u0d9a\u0dca\u200d\u0dbb\u0dd2\u0dba\u0dcf\u0dc0\u0dbd\u0dd2\u0dba\u0da7 \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba \u0d9a\u0dd2\u0dbb\u0dd3\u0db8 \u0dba\u0dd0\u0dba\u0dd2 \u0d9a\u0dd2\u0dba\u0db1\u0dd4 \u0dbd\u0dd0\u0db6\u0dda.<\/p>\r\n\r\n\r\n\r\n<p>\u0dc3\u0da7\u0dc4\u0db1 ;-<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0 C \u0d95\u0db1\u0dd1\u0db8 \u0db1\u0dd2\u0dba\u0dad\u0dba\u0d9a\u0dca \u0dc0\u0dd2\u0da7,<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\frac d{dx}\\left(g\\left(x\\right)+c\\right)&amp;=&amp;\\frac{\\displaystyle d}{\\displaystyle dx}g\\left(x\\right)+\\frac{\\displaystyle d}{\\displaystyle dx}c\\\\&amp;=&amp;f\\left(x\\right)+0\\\\&amp;=&amp;f\\left(x\\right)\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>\u0dbd\u0dd9\u0dc3 \u0dbd\u0dd0\u0db6\u0dd9\u0db1 \u0db1\u0dd2\u0dc3\u0dcf \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd3\u0db8\u0da7 \u0d85\u0db1\u0dd4\u0dc0,<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\" style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int f\\left(x\\right)dx&amp;=&amp;g\\left(x\\right)+c\\end{array}<\/span> \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0db8\u0dd9\u0dba\u0dd2\u0db1\u0dca \u0db4\u0dd0\u0dc4\u0dd0\u0daf\u0dd2\u0dbd\u0dd2 \u0dc0\u0db1\u0dca\u0db1\u0dda \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba \u0db1\u0dd2\u0dba\u0dad \u0d85\u0d9c\u0dba\u0d9a\u0dd2\u0db1\u0dca \u0dc0\u0dd9\u0db1\u0dc3\u0dca \u0dc0\u0dd2\u0dba \u0dc4\u0dd0\u0d9a\u0dd2 \u0db6\u0dc0\u0dba\u0dd2. \u0d91\u0db8 \u0db1\u0dd2\u0dc3\u0dcf \u0db8\u0dd9\u0db8 \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba \u0d85\u0db1\u0dd2\u0dc1\u0dca\u0da0\u0dd2\u0dad \u0dba\u0dd0\u0dba\u0dd2 \u0d9a\u0dd2\u0dba\u0db1\u0dd4 \u0dbd\u0dd0\u0db6\u0dda.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\"><strong>\u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0dc0\u0dca\u200d\u0dba\u0dd4\u0dad\u0dca\u0db4\u0db1\u0dca\u0db1\u0dba\u0dd9\u0db1\u0dca \u0dc3\u0dd6\u0dad\u0dca\u200d\u0dbb \u0dbd\u0db6\u0dcf \u0d9c\u0dd0\u0db1\u0dd3\u0db8<\/strong><\/h3>\r\n\r\n<ol>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l} \\frac d{dx}\\left(\\sin x\\right)=\\cos x\\Rightarrow\\int\\cos xdx=\\sin x+c\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left(\\cos x\\right)=-\\sin x\\Rightarrow\\int\\sin xdx=-\\cos x+c\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left(\\tan x\\right)=sec^2x\\Rightarrow\\int sec^2xdx=\\tan x+c\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left(-\\cos ecx\\right)=\\cos ecx.cotx\\Rightarrow\\int\\cos ecx.cotxdx=-\\cos ecx+c\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left(secx\\right)=secx.\\tan x\\Rightarrow\\int secx.\\tan xdx=secx+c\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left(-cotx\\right)=\\cos ec^2x\\Rightarrow\\int\\cos ec^2xdx=-cotx+c\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left(\\frac{x^{n+1}}{n+1}\\right)=x^n\\Rightarrow\\int x^ndx=\\frac{\\displaystyle x^{n+1}}{\\displaystyle n+1}+c\\;;n\\neq-1\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left(\\ln\\left|x\\right|\\right)=\\frac1x\\Rightarrow\\int\\frac{\\displaystyle1}{\\displaystyle x}dx=\\ln\\left|x\\right|+c\\;;\\;x\\neq0\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left[\\sin^{-1}\\left(\\frac xa\\right)\\right]=\\frac1{\\sqrt{a^2-x^2}}\\Rightarrow\\int\\frac{\\displaystyle1}{\\displaystyle\\sqrt{a^2-x^2}}dx=\\sin^{-1}\\left(\\frac{\\displaystyle x}{\\displaystyle a}\\right)+c\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left[\\tan^{-1}\\left(\\frac xa\\right)\\right]=\\frac1{x^2+a^2}\\Rightarrow\\int\\frac{\\displaystyle1}{\\displaystyle x^2+a^2}dx=\\tan^{-1}\\left(\\frac{\\displaystyle x}{\\displaystyle a}\\right)+c\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<li style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\frac d{dx}\\left(e^x\\right)=e^x\\Rightarrow\\int e^xdx=e^x+c\\\\\\\\\\\\\\\\\\end{array}<\/span><\/li>\r\n<\/ol>\r\n\r\n<ul class=\"wp-block-list\">\r\n<li>\u0d89\u0dc4\u0dad \u0dc3\u0db8\u0dd3\u0d9a\u0dbb\u0dab \u0dc0\u0dbd x \u0dc4\u0dd0\u0dbb \u0dc0\u0dd2\u0da0\u0dbd\u0dca\u200d\u0dba \u0db1\u0dd0\u0dad.<\/li>\r\n<li>\u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba \u0db4\u0dcf\u0da9\u0db8\u0dda\u0daf\u0dd3 \u0d89\u0daf\u0dd2\u0dbb\u0dd2\u0dba\u0da7 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4 \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8\u0da7 \u0d89\u0dc4\u0dad \u0dc3\u0dd6\u0dad\u0dca\u200d\u0dbb \u0db8\u0dad\u0d9a \u0dad\u0db6\u0dcf \u0d9c\u0dad \u0dba\u0dd4\u0dad\u0dd4\u0dba\u0dd2.<\/li>\r\n<\/ul>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\"><strong>\u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba\u0dda\u00a0 \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba\u0db1\u0dca<\/strong><\/h3>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\int\\;kf(x)dx=k\\int\\;f(x)dx<\/span><\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\int{f(x)\\pm g(x)}dx=\\int f(x)dx\\pm\\int g(x)dx<\/span><\/p>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n\r\n\r\n<h4 class=\"wp-block-heading\"><strong>\u0db4\u0dc4\u0dad \u0d9c\u0dd0\u0da7\u0dc5\u0dd4 \u0dc0\u0dd2\u0dc3\u0db3\u0db8\u0dd4<\/strong><\/h4>\r\n\r\n\r\n\r\n<p>\u00a01)<span class=\"wp-katex-eq\" data-display=\"false\">\\int2\\sin xdx=2\\int\\sin xdx=-2\\cos x+c<\/span><\/p>\r\n\r\n\r\n\r\n<p>2)<span class=\"wp-katex-eq\" data-display=\"false\">\\int\\frac3xdx=3\\int\\frac1xdx=3\\ln\\left|x\\right|+c<\/span><\/p>\r\n\r\n\r\n\r\n<p>3)<span class=\"wp-katex-eq\" data-display=\"false\">\\int3\\cos ecx.cotxdx=-3\\cos ec^2x+c<\/span><\/p>\r\n\r\n\r\n\r\n<p>4)<span class=\"wp-katex-eq\" data-display=\"false\">\\int kdx=k\\int dx=kx+c<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d89\u0dc4\u0dad \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba\u0dda \u0dba\u0ddc\u0daf\u0dcf \u0d9c\u0dd0\u0db1\u0dd9\u0db1\u0dca\u0db1\u0dda <span class=\"wp-katex-eq\" data-display=\"false\">\\int_{}^{}x^{n}dx=\\frac{x^{n+1}}{n+1}+c<\/span>\u00a0\u0dc3\u0dd6\u0dad\u0dca\u200d\u0dbb\u0dba\u0dda\u0db8 n=0 \u0d85\u0dc0\u0dc3\u0dca\u0dae\u0dcf\u0dc0 \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<p>5)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\left(2x-\\frac3x\\right)dx&amp;=&amp;2\\int xdx-3\\int\\frac1xdx\\\\&amp;=&amp;2\\frac{x^2}2+3\\ln\\left|x\\right|+c\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>6)<span class=\"wp-katex-eq\" data-display=\"false\">\\int(2\\sin x-3\\cos x+4)dx=2\\int\\sin xdx-3\\int\\cos xdx+4\\int dx=-2\\cos x-3\\sin x+4x<\/span><\/p>\r\n\r\n\r\n\r\n<p>7)<span class=\"wp-katex-eq\" data-display=\"false\">\\int\\left(2e^x-5\\right)dx=2\\int e^xdx-5\\int dx=2e^x-5x+c<\/span><\/p>\r\n\r\n\r\n\r\n<p>8)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac3{x^2+25}dx&amp;=&amp;\\int\\frac{\\displaystyle3}{\\displaystyle x^2+5^2}dx\\\\&amp;=&amp;\\frac35\\tan^{-1}\\left(\\frac x5\\right)+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>9)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\tan^2xdx&amp;=&amp;\\int(sec^2x-1)dx\\\\&amp;=&amp;\\int sec^2xdx-\\int dx\\\\&amp;=&amp;\\tan x-x+c\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>10)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int cot^2xdx&amp;=&amp;\\int(\\cos ec^2x-1)dx\\\\&amp;=&amp;\\int\\cos ec^2xdx-\\int dx\\\\&amp;=&amp;-cotx-x+c\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>11)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac5{\\sqrt{9-x^2}}dx&amp;=&amp;5\\int\\frac1{\\sqrt{3^2-x^2}}dx\\\\&amp;=&amp;5\\sin^{-1}\\left(\\frac x3\\right)+c\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>12)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int3\\cos ecx.cotxdx&amp;=&amp;3\\int\\cos ecx.cotxdx\\\\&amp;=&amp;-3\\cos ecx+c\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d89\u0dc4\u0dad \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0dc0\u0dca\u200d\u0dba\u0dd4\u0dad\u0dca\u0db4\u0db1\u0dca\u0db1\u0dba\u0dd9\u0db1\u0dca \u0dbd\u0db6\u0dcf\u0d9c\u0dad\u0dca \u0dc3\u0dd6\u0dad\u0dca\u200d\u0dbb \u0dc0\u0dbd\u0da7 \u0d85\u0db8\u0dad\u0dbb\u0dc0 \u0db8\u0dd9\u0db8 \u0db4\u0dc4\u0dad\u0dd2\u0db1\u0dca \u0daf\u0d9a\u0dca\u0dc0\u0dcf \u0d87\u0dad\u0dd2 \u0dc3\u0dd6\u0dad\u0dca\u200d\u0dbb \u0daf\u0dd9\u0d9a\u0dad\u0dca \u0db8\u0dad\u0d9a\u0dba\u0dda \u0dad\u0db6\u0dcf \u0d9c\u0dd0\u0db1\u0dd3\u0db8\u0dd9\u0db1\u0dca \u0d9c\u0dd0\u0da7\u0dc5\u0dd4 \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8\u0da7 \u0db4\u0dc4\u0dc3\u0dd4\u0dc0\u0d9a\u0dca \u0d87\u0dad. \u0db1\u0db8\u0dd4\u0dad\u0dca \u0db8\u0dd9\u0db8 \u0dc3\u0dd6\u0dad\u0dca\u200d\u0dbb \u0daf\u0dd9\u0d9a \u0dba\u0ddc\u0daf\u0dcf\u0d9c\u0dd0\u0db1\u0dd9\u0db1 \u0d9c\u0dd0\u0da7\u0dc5\u0dd4 \u0dc0\u0dd2\u0dc3\u0db3\u0dd3\u0db8 \u0dc3\u0db3\u0dc4\u0dcf \u0d86\u0daf\u0dda\u0dc1 \u0d9a\u0dd2\u0dbb\u0dd3\u0db8\u0dca \u0daf \u0dba\u0ddc\u0daf\u0dcf \u0d9c\u0db1\u0dca\u0db1\u0dcf \u0d86\u0d9a\u0dcf\u0dbb\u0dba \u0db4\u0dcf\u0da9\u0db8\u0dd9\u0dc4\u0dd2 \u0db4\u0dc3\u0dd4\u0dc0 \u0dc3\u0dcf\u0d9a\u0da0\u0dca\u0da1\u0dcf \u0d9a\u0dd9\u0dbb\u0dda.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\frac d{dx}\\left(\\ln\\left|x+\\sqrt{x^2-a^2}\\right|\\right)&amp;=&amp;\\frac1{\\sqrt{x^2-a^2}}\\Rightarrow\\int\\frac{\\displaystyle1}{\\displaystyle\\sqrt{x^2-a^2}}dx=\\ln\\left|x+\\sqrt{x^2-a^2}\\right|+c\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\frac d{dx}\\left(\\ln\\left|x+\\sqrt{x^2+a^2}\\right|\\right)&amp;=&amp;\\frac1{\\sqrt{x^2+a^2}}\\Rightarrow\\int\\frac{\\displaystyle1}{\\displaystyle\\sqrt{x^2+a^2}}dx=\\ln\\left|x+\\sqrt{x^2+a^2}\\right|+c\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf: <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac{\\displaystyle2}{\\displaystyle\\sqrt{x^2-16}}d&amp;=&amp;2\\int\\frac{\\displaystyle dx}{\\displaystyle\\sqrt{x^2-4^2}}\\\\&amp;=&amp;2\\ln\\left|x+\\sqrt{x^2-4^2}\\right|+c\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{c}\\int\\frac{\\displaystyle3dx}{\\sqrt{5-x^2}}=3\\int\\frac{\\displaystyle dx}{\\sqrt{x^2+(\\sqrt5)^2}}\\\\=3ln\\left|x+\\sqrt{x^2+(\\sqrt5)^2}\\right|+c\\end{array}<\/span>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\"><strong><span class=\"td_text_columns_two_cols\">\u00a0x \u0dc4\u0dd2 \u0dbb\u0dda\u0d9b\u0dd3\u0dba \u0db4\u0dca\u200d\u0dbb\u0d9a\u0dcf\u0dc1 \u0d87\u0dad\u0dd2 \u0dc1\u0dca\u200d\u0dbb\u0dd2\u0dad \u0dc0\u0dbd \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba<\/span><\/strong><\/h3>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int f\\left(x\\right)dx&amp;=&amp;g\\left(x\\right)+c\\end{array}<\/span>\u00a0\u0db1\u0db8\u0dca,<\/p>\r\n\r\n\r\n\r\n<p><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int f\\left(ax+b\\right)dx&amp;=&amp;\\frac1ag(ax+b)+c\\;\\end{array}<\/span><strong> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ( c<\/strong>&#8211; \u0d85\u0db7\u0dd2\u0db8\u0dad \u0db1\u0dd2\u0dba\u0dad\u0dba )<\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u0dc3\u0dcf\u0db0\u0db1\u0dba:-<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}{\\frac d{dx}\\left[\\frac1ag(ax+b)+c\\right]\\;}&amp;=&amp;\\int\\frac1af(ax+b).a\\\\&amp;=&amp;{f(ax+b)}\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab :-<\/p>\r\n\r\n\r\n\r\n<p>1.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\left(2x+1\\right)^2dx&amp;=&amp;\\frac13\\left(2x+1\\right)^3.\\frac12+c\\\\&amp;=&amp;\\frac16\\left(2x+1\\right)^3+c\\end{array}<\/span> <strong>( c<\/strong>&#8211; \u0d85\u0db7\u0dd2\u0db8\u0dad \u0db1\u0dd2\u0dba\u0dad\u0dba )<\/p>\r\n\r\n\r\n\r\n<p>2.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\;\\sin(\\;5x\\;+\\;1\\;)\\;dx\\;\\;&amp;=&amp;-\\;\\frac15\\;\\cos\\;(\\;5x\\;+\\;1\\;)\\;+\\;c\\;\\;\\end{array}<\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0( c- \u0d85\u0db7\u0dd2\u0db8\u0dad \u0db1\u0dd2\u0dba\u0dad\u0dba )<\/p>\r\n\r\n\r\n\r\n<p>3.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\;\\sin(\\;5x\\;+\\;1\\;)\\;dx\\;\\;&amp;=&amp;-\\;\\frac15\\;\\cos\\;(\\;5x\\;+\\;1\\;)\\;+\\;c\\;\\;\\end{array}<\/span> \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0( c- \u0d85\u0db7\u0dd2\u0db8\u0dad \u0db1\u0dd2\u0dba\u0dad\u0dba )<\/p>\r\n\r\n\r\n\r\n<p>4.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int e^{5x+2}dx&amp;=&amp;\\frac15e^{5x+2}+c\\end{array}<\/span> ( c- \u0d85\u0db7\u0dd2\u0db8\u0dad \u0db1\u0dd2\u0dba\u0dad\u0dba )<\/p>\r\n\r\n\r\n\r\n<p>5.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac1{4x-3}dx&amp;=&amp;\\frac14\\ln\\left|4x-3\\right|+c\\end{array}<\/span> ( c- \u0d85\u0db7\u0dd2\u0db8\u0dad \u0db1\u0dd2\u0dba\u0dad\u0dba )<\/p>\r\n\r\n\r\n\r\n<p>6.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int sec^2\\left(3x+5\\right)dx&amp;=&amp;\\frac13\\tan\\left(3x+5\\right)+c\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>7.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac1{\\sqrt{1-49x^2}}dx&amp;=&amp;\\int\\frac1{\\sqrt{1-\\left(7x\\right)^2}}dx\\\\&amp;=&amp;\\frac17\\sin^{-1}\\left(7x\\right)+c\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>8.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac1{\\sqrt{25+4x^2}}dx&amp;=&amp;\\int\\frac1{\\sqrt{5^2+\\left(2x\\right)^2}}dx\\\\&amp;=&amp;\\frac12\\ln\\left|2x+\\sqrt{\\left(2x\\right)^2+5^2}\\right|+c\\\\&amp;=&amp;\\frac12\\ln\\left|2x+\\sqrt{4x^2+25}\\right|+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>9.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\sin2x.\\cos3xdx&amp;=&amp;\\frac12\\int\\left(\\sin5x-\\sin x\\right)dx\\\\&amp;=&amp;\\frac12\\int\\sin5xdx-\\frac12\\int\\sin xdx\\\\&amp;=&amp;\\frac1{10}\\cos5x+\\frac12\\cos x+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>10.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\cos4x.\\cos5xdx&amp;=&amp;\\frac12\\int\\left(\\cos9x+\\cos x\\right)dx\\\\&amp;=&amp;\\frac12\\int\\cos9xdx+\\frac12\\int\\cos xdx\\\\&amp;=&amp;\\frac1{18}\\sin9x+\\frac12\\sin x+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>11.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int3\\sin6x\\sin2xdx&amp;=&amp;\\int3\\left(-\\frac12\\right)\\left(\\cos8x-\\cos4x\\right)dx\\\\&amp;=&amp;-\\frac32\\int\\cos8xdx+\\frac32\\int\\cos4xdx\\\\&amp;=&amp;\\frac3{16}\\sin8x-\\frac38\\sin4x+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>12.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\sin^23xdx&amp;=&amp;\\frac12\\int\\left[1-\\cos6x\\right]dx\\\\&amp;=&amp;\\frac{\\displaystyle1}{\\displaystyle2}\\int dx-\\frac12\\int\\cos6xdx\\\\&amp;=&amp;\\frac{\\displaystyle1}{\\displaystyle2}x-\\frac1{12}\\sin6x+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n<p>13.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int5\\cos^2\\left(2x-1\\right)dx&amp;=&amp;\\int\\frac52\\left\\{1-\\cos\\left[2\\left(2x-1\\right)\\right]\\right\\}dx\\\\&amp;=&amp;\\frac52\\int dx-\\frac52\\int\\cos\\left(4x-2\\right)dx\\\\&amp;=&amp;\\frac{25}{16}\\cos\\left(4x-2\\right)+c\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n<p>14.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\int\\sin^3xdx\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{l}\\sin3x\\equiv3\\sin x-4\\sin^3x\\\\\\sin^3x\\equiv\\frac14\\left(3\\sin x-\\sin3x\\right)\\end{array}<\/span>\r\n\r\n\r\n\r\n<p style=\"text-align: left\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\sin^3xdx&amp;=&amp;\\frac14\\int\\left(3\\sin x-\\sin3x\\right)dx\\\\&amp;=&amp;\\frac34\\int\\sin xdx-\\frac14\\int\\sin3xdx\\\\&amp;=&amp;-\\frac34\\cos x+\\frac1{12}\\cos3x+c\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>15.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\int\\cos^32xdx\\end{array}<\/span><\/p>\r\n\r\n<p>16.<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\cos6x&amp;\\equiv&amp;4\\cos^3x2x-3\\cos2x\\\\\\cos^32x&amp;\\equiv&amp;\\frac14\\left(\\cos6x-3\\cos2x\\right)\\\\\\int\\cos^32x&amp;=&amp;\\frac14\\int\\left(\\cos6x-3\\cos2x\\right)dx\\\\&amp;=&amp;\\frac14\\int\\cos6xdx-\\frac34\\int\\cos2xdx\\\\&amp;=&amp;-\\frac1{24}\\sin6x+\\frac38\\sin2x+c\\end{array}<\/span><\/p>\r\n\r\n<p>sinx \u0dc4\u0dcf cosx \u0dc0\u0dbd \u0db6\u0dbd\u0dba\u0db1\u0dca \u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba \u0d9a\u0dd2\u0dbb\u0dca\u200d\u0dbb\u0dd2\u0db8 \u0dc3\u0db3\u0dc4\u0dcf \u0dad\u0dc0\u0dad\u0dca \u0d9a\u0dca\u200d\u0dbb\u0db8\u0dba\u0d9a\u0dca \u0db8\u0dd9\u0db8 \u0db4\u0dcf\u0da9\u0db8\u0dda \u0db4\u0dc3\u0dd4\u0dc0 \u0dc3\u0dcf\u0d9a\u0da0\u0dca\u0da1\u0dcf \u0d9a\u0dd9\u0dbb\u0dda.<\/p>\r\n\r\n\r\n\r\n<h3 class=\"wp-block-heading\"><strong>\u0dbd\u0db6\u0dca\u0db0\u0dd2\u0dba\u0d9a\u0dca \u0d86\u0d9a\u0dbb\u0dba\u0dda \u0d85\u0db1\u0dd4\u0d9a\u0dbd \u0dc0\u0dbd\u0daf\u0dd3 \u0dc0\u0dd0\u0daf\u0d9c\u0dad\u0dca \u0dc0\u0db1 <\/strong><strong>\u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba\u0d9a\u0dca<\/strong><\/h3>\r\n\r\n\r\n\r\n<p>\u0dc4\u0dbb\u0dba\u0dda \u0d85\u0dc0\u0d9a\u0dbd\u0db1 \u0dc3\u0d82\u0d9c\u0dd4\u0dab\u0d9a\u0dba \u0dbd\u0dc0\u0dba\u0dda \u0d87\u0dad\u0dca\u0db1\u0db8\u0dca \u0dc4\u0ddd \u0dbd\u0dc0\u0dba\u0dda \u0db1\u0dd2\u0dbb\u0dca\u0db8\u0dcf\u0dab\u0dba \u0d9a\u0dbd \u0dc4\u0dd0\u0d9a\u0dd2 \u0db1\u0db8\u0dca \u0db8\u0dd9\u0db8 \u0d9a\u0dca\u200d\u0dbb\u0db8\u0dba \u0dba\u0ddd\u0d9c\u0dca\u200d\u0dba \u0dc0\u0dda.<\/p>\r\n\r\n\r\n\r\n<p class=\"has-text-align-center\"><span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}&amp;&amp;\\\\int\\frac{f&#039;\\left(x\\right)}{f\\left(x\\right)}dx&amp;=&amp;\\ln\\left|f\\left(x\\right)\\right|+c\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u00a0\u0dc3\u0dcf\u0db0\u0db1\u0dba:- <span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\frac d{dx}\\left[\\ln\\left|f\\left(x\\right)\\right|+c\\right]&amp;=&amp;\\int\\frac{f&#039;\\left(x\\right)}{f\\left(x\\right)}+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n\r\n\r\n\r\n<p>\u0d85\u0db1\u0dd4\u0d9a\u0dbd\u0db1\u0dba\u0dda \u0d85\u0dbb\u0dca\u0dae \u0daf\u0dd0\u0d9a\u0dca\u0dc0\u0dd3\u0db8\u0da7 \u0d85\u0db1\u0dd4\u0dc0,<\/p>\r\n\r\n\r\n\r\n<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac{f&#039;\\left(x\\right)}{f\\left(x\\right)}dx&amp;=&amp;\\ln\\left|f\\left(x\\right)\\right|+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span>\r\n\r\n\r\n\r\n<p>\u0d8b\u0daf\u0dcf\u0dc4\u0dbb\u0dab:-<\/p>\r\n\r\n\r\n\r\n<ul class=\"wp-block-list\" type=\"1\">\r\n<li>1)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac{\\sin x-\\cos x}{\\sin x+\\cos x}dx&amp;=&amp;-\\int\\frac{\\displaystyle\\cos x-\\sin x}{\\displaystyle\\sin x+\\cos x}\\\\&amp;=&amp;-\\ln\\left|\\sin x+\\cos x\\right|+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span> <strong>( <\/strong>c- \u0d85\u0db7\u0dd2\u0db8\u0dad \u0db1\u0dd2\u0dba\u0dad\u0dba )<\/li>\r\n<\/ul>\r\n\r\n<p>2)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac{x+1}{x^2+2x+5}dx&amp;=&amp;\\frac12\\int\\frac{2x+2}{x^2+2x+5}dx\\\\&amp;=&amp;\\frac12\\ln\\left|x^2+2x+5\\right|+c\\\\&amp;&amp;\\\\&amp;&amp;\\\\&amp;&amp;\\end{array}<\/span><\/p>\r\n<p>3)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\tan xdx&amp;=&amp;\\int\\frac{\\sin{\\displaystyle x}}{\\cos{\\displaystyle x}}dx\\\\&amp;=&amp;-\\int\\left(\\frac{\\displaystyle-\\sin x}{\\cos{\\displaystyle x}}\\right)dx\\\\&amp;=&amp;-\\ln\\left|\\cos x\\right|+c\\end{array}<\/span><\/p>\r\n<p>4)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int cotxdx&amp;=&amp;\\int\\frac{\\cos x}{\\sin x}dx\\\\&amp;=&amp;\\ln\\left|\\sin x\\right|+c\\end{array}<\/span><\/p>\r\n<p>5)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int secxdx&amp;=&amp;\\int\\frac{secx\\left(secx+\\tan x\\right)}{\\left(secx+\\tan x\\right)}dx\\\\&amp;=&amp;\\ln\\left|secx+\\tan x\\right|+c\\end{array}<\/span><\/p>\r\n<p>6)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\cos ecxdx&amp;=&amp;-\\int\\left(-\\frac{\\cos ecx\\left(\\cos ecx+cotx\\right)}{\\left(\\cos ecx+cotx\\right)}\\right)dx\\\\&amp;=&amp;-\\ln\\left|\\cos ecx+cotx\\right|+c\\end{array}<\/span><\/p>\r\n<p>7)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac1{x\\left(x^{2020}+1\\right)}dx&amp;=&amp;\\int\\frac{\\left(x^{2020}+1\\right){\\displaystyle-}{\\displaystyle{\\displaystyle x}^{2020}}}{x\\left(x^{2020}+1\\right)}dx\\\\&amp;=&amp;\\int\\frac1xdx-\\int\\frac{x^{2019}}{\\left(x^{2020}+1\\right)}dx\\\\&amp;=&amp;\\ln\\left|x\\right|-\\frac{\\ln{\\displaystyle\\left|x^{2020}+1\\right|}}{2020}+c\\end{array}<\/span><\/p>\r\n<p>8)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac1{x\\ln\\left|x\\right|}dx&amp;=&amp;\\ln\\left|\\ln\\left|x\\right|\\right|+c\\end{array}<\/span><\/p>\r\n<p>9)<span class=\"wp-katex-eq\" data-display=\"false\">\\begin{array}{rcl}\\int\\frac1{1+e^x}dx&amp;=&amp;-\\int\\frac{e^{-x}}{1+e^{-x}}dx\\\\&amp;=&amp;-\\ln\\left|1+e^{-x}\\right|+c\\end{array}<\/span><\/p>\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\r\n<div class=\"wp-block-embed__wrapper\">https:\/\/youtu.be\/Wxx8oMNPlIA<\/div>\r\n<\/figure>\r\n\r\n\r\n\r\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\">\r\n<div class=\"wp-block-embed__wrapper\">https:\/\/youtu.be\/AJ8fGN6HGWM<\/div>\r\n<\/figure>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n\r\n\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/uc?id=1zaYSXmmKtEI7L634oT3ufxFF4YbXDqbX&amp;export=download\" target=\"_blank\" rel=\"noreferrer noopener\">\u0db4\u0dcf\u0da9\u0db8\u0dda \u0dc3\u0da7\u0dc4\u0db1 Download \u0d9a\u0dbb\u0d9c\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-block-buttons-is-layout-flex\">\r\n<div class=\"wp-block-button is-style-shadow td_btn_normal\"><a class=\"wp-block-button__link\" style=\"border-radius: 15px\" href=\"https:\/\/drive.google.com\/drive\/folders\/1nckWIt5wB-xVw56bK1UE2TWCsXw7jlNl?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\">\u0dad\u0dc0\u0dad\u0dca \u0db4\u0dca\u200d\u0dbb\u0dc1\u0dca\u0db1 \u0db4\u0dd9\u0db1\u0dca\u0dc0\u0db1\u0dca\u0db1.<\/a><\/div>\r\n<\/div>\r\n\r\n\r\n\r\n<div class=\"wp-block-spacer\" style=\"height: 100px\" aria-hidden=\"true\">\u00a0<\/div>\r\n\r\n\r\n\r\n<p>&nbsp;<\/p>\r\n","protected":false},"excerpt":{"rendered":"<p>\u0dc0\u0dca\u200d\u0dba\u0dd4\u0dad\u0dca\u0db4\u0db1\u0dca\u0db1 \u0db4\u0dd2\u0dc5\u0dd2\u0db6\u0daf \u0db4\u0dca\u200d\u0dbb\u0dad\u0dd2\u0db5\u0dbd \u0db7\u0dcf\u0dc0\u0dd2\u0dad\u0dba\u0dd9\u0db1\u0dca \u0d85\u0db1\u0dd2\u0dc1\u0dca\u0da0\u0dd2\u0dad \u0d85\u0db1\u0dd4\u0d9a\u0dbd \u0dc3\u0dd9\u0dc0\u0dd3\u0db8 \u0dc4\u0dcf \u0d85\u0db1\u0dd4\u0d9a\u0dbd \u0db4\u0dca\u200d\u0dbb\u0db8\u0dda\u0dba\u0dba\u0db1\u0dca \u0db8\u0dd9\u0db8 \u0db4\u0dcf\u0da9\u0db8\u0dda \u0d85\u0db1\u0dca\u0dad\u0dbb\u0dca\u0d9c\u0dad \u0dc0\u0dda. <\/p>\n","protected":false},"author":67,"featured_media":16557,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"tdm_status":"","tdm_grid_status":"","footnotes":""},"categories":[3671,3635,42,3630,3629],"tags":[3701,4008,4011,4012,4019,4020,4022,4009,3698,3699,4007,4021,4015,4014,4017,3703,4010,3702,4013,4016],"class_list":{"0":"post-11574","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-04-05-integration","8":"category-04-calculus","9":"category-advanced-level-science","10":"category-pure-mathematics","11":"category-combined-mathematics","12":"tag-anukalanaya","13":"tag-anukalanaya-artha-dakweema","14":"tag-anukalanaya-hadhinweema-saha-mulika-prameyan","15":"tag-anukalanaya-hadinweema-saha-mulika-prameyan","16":"tag-anukalanaya-prameeyan","17":"tag-anukalanaya-prameyan","18":"tag-anukhalanaya","19":"tag-calcules","20":"tag-calculus","21":"tag-kalanaya","22":"tag-kalanya","23":"tag-labdhiyak-akara-anukalana-waladi-wadagath-wana-prameyan","24":"tag-prathi-wiyuthpanna-suthra-laba-ganeema","25":"tag-prathiwiyuthpanna-suthra-laba-ganima","26":"tag-x-----","27":"tag-3703","28":"tag-4010","29":"tag-3702","30":"tag-4013","31":"tag-4016"},"_links":{"self":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/11574"}],"collection":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/users\/67"}],"replies":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/comments?post=11574"}],"version-history":[{"count":33,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/11574\/revisions"}],"predecessor-version":[{"id":32576,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/posts\/11574\/revisions\/32576"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media\/16557"}],"wp:attachment":[{"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/media?parent=11574"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/categories?post=11574"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/learnsteer.sasnaka.org\/science\/wp-json\/wp\/v2\/tags?post=11574"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}