Here you will learn Integration integration formulas for class 12.<\/p>\n
Let’s begin –<\/p>\n
(i)\u00a0 \\(\\int\\) \\({(ax+b)}^n\\) dx = \\({(ax+b)}^{n+1}\\over {a(n+1)}\\) + C ; n \\(\\ne\\) -1<\/p>\n
(ii)\u00a0 \\(\\int\\) \\(dx\\over {ax+b}\\) dx = \\(1\\over a\\) ln|ax+b| + C<\/p>\n
(iii)\u00a0 \\(\\int\\) \\(e^{ax+b}\\) dx = \\({1\\over {a}}e^{ax+b}\\) + C or \\(\\int\\) \\(e^x\\) = \\(e^x\\) + C<\/p>\n
(iv)\u00a0 \\(\\int\\) \\(a^{px+q}\\) dx = \\({1\\over p}\\) \\({a^{px+q}}\\over lna\\) + C, (a > 0)<\/p>\n
(v)\u00a0 \\(\\int\\) sinx dx = -cosx + C<\/p>\n
(vi)\u00a0 \\(\\int\\) cosx dx = sinx + C<\/p>\n
(vii)\u00a0 \u00a0\\(\\int\\) tanx dx = ln|secx| + C<\/p>\n
(viii)\u00a0 \\(\\int\\) cotx dx = ln|sinx| + C<\/p>\n
(ix)\u00a0 \\(\\int\\) \\(sec^2x\\) dx = tanx + C<\/p>\n
(x)\u00a0 \\(\\int\\) \\(cosec^2x\\) dx = -cotx + C<\/p>\n
(xi)\u00a0 \\(\\int\\) cosecx.cotx dx = -cosecx + C<\/p>\n
(xii)\u00a0 \\(\\int\\) secx.tanx dx = secx + C<\/p>\n
(xiii)\u00a0 \\(\\int\\) secx dx = ln|secx+tanx| + C = ln|tan(\\(\\pi\\over 4\\) + \\(x\\over 2\\))| + C<\/p>\n
(xiv)\u00a0 \\(\\int\\) cosecx dx = ln|cosecx-cotx| + C = ln|tan\\(x\\over 2\\)| = -ln|cosecx+cotx| + C<\/p>\n
(xv)\u00a0 \\(\\int\\) \\(dx\\over {\\sqrt{a^2-x^2}}\\) = \\(sin^{-1} {x\\over a}\\) + C<\/p>\n
(xvi)\u00a0 \\(\\int\\) \\(dx\\over {a^2+x^2}\\) = \\(1\\over a\\) \\(tan^{-1} {x\\over a}\\) + C<\/p>\n
(xvii)\u00a0 \\(\\int\\) \\(dx\\over {x\\sqrt{x^2-a^2}}\\) = \\(1\\over a\\) \\(sec^{-1} {x\\over a}\\) + C<\/p>\n
(xviii) \\(\\int\\) \\(dx\\over {\\sqrt{x^2+a^2}}\\) = \\(ln[x+\\sqrt{x^2+a^2}]\\) + C<\/p>\n
(xix)\u00a0 \\(\\int\\) \\(dx\\over {\\sqrt{x^2-a^2}}\\) = \\(ln[x+\\sqrt{x^2-a^2}]\\) + C<\/p>\n
(xx)\u00a0 \\(\\int\\) \\(dx\\over {a^2-x^2}\\) = \\(1\\over 2a\\) \\(ln|{a+x\\over {a-x}}|\\) + C<\/p>\n
(xxi)\u00a0 \\(\\int\\) \\(dx\\over {x^2-a^2}\\) = \\(1\\over 2a\\) \\(ln|{x-a\\over {x+a}}|\\) + C<\/p>\n
(xxii)\u00a0 \\(\\int\\) \\(\\sqrt{a^2-x^2}\\) dx = \\(x\\over 2\\)\\(\\sqrt{a^2-x^2}\\) + \\(a^2\\over 2\\) \\(sin^{-1} {x\\over a}\\) + C<\/p>\n
(xxii)\u00a0 \\(\\int\\) \\(\\sqrt{x^2+a^2}\\) dx = \\(x\\over 2\\)\\(\\sqrt{x^2+a^2}\\) + \\(a^2\\over 2\\) \\(ln[x+\\sqrt{x^2+a^2}]\\) + C<\/p>\n
(xxii)\u00a0 \\(\\int\\) \\(\\sqrt{x^2-a^2}\\) dx = \\(x\\over 2\\)\\(\\sqrt{x^2-a^2}\\) – \\(a^2\\over 2\\) \\(ln[x+\\sqrt{x^2-a^2}]\\) + C<\/p>\n
Hope you learnt integration formulas for class 12, learn more concepts of integration and practice more questions to get ahead in competition. Good Luck!<\/p>\n\n\n